On the 1901 census she is clearly given as aged 30 which is virtually impossible for her marriage in 1883.

She was living at Fair Oak Lodge and had her sister with her husband with her.  Her brother in law (which he was twice as he was also the half brother of her late husband) was down as Sir Arthur Grant and her sister as "Lady Grant" and then got herself classified as a "Lady Help, Domestic"!

Additionally in 1901 she was classified as a landowner living on own means and had five living in servants.
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On FreeBMD there is an Edith Gillett who d. aged 80 in Q1 of 1914 in Weymouth district, vol 5a, p. 418.  It could be her, but not sure.
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The 1881 census births of Edith Douglases from 1825 to 1865 are:

1. Edith DOUGLAS - 1881 British Census / Middlesex
Visitor   Gender: Female   Birth: <1854> Abbotsley, Huntingdon, England
2. Edith DOUGLASS - 1881 British Census / Worcester
Visitor   Gender: Female   Birth: <1859> Claybrook, Leicester, England
3. Edith A. DOUGLAS - 1881 British Census / Lancashire
Daur   Gender: Female   Birth: <1861> Manchester, Lancashire, England
4. Edith A.B. DOUGLAS - 1881 British Census / Nottingham
Visitor   Gender: Female   Birth: <1863> Haddington, Scotland

The second of these might be her, having the Claybrook, Leics birth place of some previous information, probably the 1901 census.  She might have been staying with the Smiths as a friend of their daughter Constance G Smith.

But the only Edith Douglas on FreeBMD births between 1855 and 1864 was born in 1860 in the Chorlton, Lancs district.  Not very likely to be her.
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Further I have looked her up on the 1881 census as that includes Scotland.  I think this was her:

Edith A B Douglas, aged 18, born in Haddington, Scotland and an Advocate’s daughter.

Now to see if I can find her father and if he was an advocate.

No.  Though the Henry Sholto I have found was a Magistrate and a DL of Leics, living at West End Road, South Stoneham, Hants, aged 60.   Neither of his daus Edith or Mary were at home.  Is this the right family?  But this address makes sense with the marriage at Bitterne which is near South Stoneham.
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In 1911 she had two sisters with her:

Name  Relation  Condition/Yrs married  Sex  Age  Birth Year  Occupation  Where Born

GILLETT, Edith Head Widow F 45 1866 Private mean Lutterworth Leicestershire
DOUGLAS, Annie Sister Single F 58 1853 Private means  Cheltenham Gloucester
CAMPBELL, Constance Sister Married F 45 1866  Lutterworth Leicesteshire
SMITH, Annie     Servant Single F 40 1871  Maid Domestic  Baughurst Hants
BARBER, Rose Louise Servant Single F 35 1876  Cook Domestic  West End Hants
MILLS, Susan Emma Servant Single F 31 1880  Palour Maid Domestic  Swaythling Hants
POINTER, Elsie Mary Servant Single F 15 1896  Housemaid Domestic  Southampton Hants

RG number: RG14 Piece: 6052 Reference: RG14PN6052 RG78PN276 RD100 SD2 ED4 SN2

Registration District: South Stoneham
Sub District: South Stoneham
EnumerationDistrict: 4
Parish: West End

Address: Westend Lodge Westend Near Southampton
County: Hampshire
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These deaths are of the right age:

Surname   First name(s)   Age   District   Vol  Page
Deaths Sep 1919   (>99%)
GILLETT Edith 55 Haslingden 8e 122
Deaths Sep 1939   (>99%)
Gillett Edith J 74 Abingdon 2c 392
Deaths Mar 1954   (99%)
Gillett Edith B 90 Croydon 5g 116

None of them are convincingly her.  No Edith Gillett deaths found in Scotland.
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2015, TFPL: This death does look like hers, because so many Trotter connections ended up in Bournemouth, though I’m not sure where he second name of ‘A’ came from:

Surname First name(s) Age District Vol Page
Deaths Dec 1941   (>99%)
Gillett Edith A 74 Bournemouth 2b 1497

But probate was given to a Winifred Gillett and I can find no connection to such.
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The marriage record on the BMD Index is:
Apr-Jun 1883, William Arthur GILLETT, S. Stoneham, 2c 76

Here is Rosemary Webb's transcript of a newspaper (unknown) report of the wedding:

BITTERNE, JUNE 13 1883

FASHIONABLE WEDDING

A numerous and fashionable company assembled at St Saviour's Church, Bitterne, on Wednesday, when Mr William Arthur Gillett, son of Mr W S Gillett, of Harefield, was married to Edith, daughter of Captain H. Sholto Douglas, of Moorlands, late 42nd Royal Highlanders (Black Watch), and granddaughter of the late Major General Sir Wm. Douglas, K.C.H of Timpendean, Roxburghshire.  The ceremony was performed by the Rev. H.E. Trotter.  The bride, who was given away by her father, wore bodice and train of white brocade, over a petticoat of satin, with handsome pearl embroidery, wreath and spray of orange blossoms, with tulle veil.  The bridesmaids were Miss Constance Douglas, Miss Ethel Douglas, and Miss Florence Douglas, sisters of the bride, and her cousin, Miss Constance Smith (this is my great aunt!)  (In the margin a further name is added to the bridesmaids:  Miss G. Beadon).  They wore cream surah dresses, with ficelle lace, white bonnets trimmed with wreath of Parma violets, and bouquets and gold bangles, the gift of the bridegroom.  Mr H Loxley was best man, and the groomsmen Colonel Murray (a cousin of Constance Smith), Major Douglas, Mr F Murray (Miss Constance Smith's uncle) and Mr C Douglas.  The day was beautifully fine, and considerable interest was evinced in the ceremony, after which a large company were entertained at Moorlands (the house no longer exists, but apparently the gatehouse does).  The happy couple left early in the afternoon, amidst the customary showers of rice and expressions of hearty good wishes, for London, en route for the Lakes, where the honeymoon will be spent.  The bride's travelling dress was electric blue satin merveilleux and cashmere, with bonnet to match.

Amongst the presents, which were numerous and costly were the following:-

Diamond hoop ring and travelling case, the bridegroom.
Silver coffee pot, teapot, sugar basin, and cream jug, Miss Grant.
Silver saltcellars,  Mr and Mrs Douglas Murray
Pair of ivory brushes and silver eggstand, Mrs Campbell.
Velvet and plush table, Colonel Bailie
Brass inkstand and morocco writing and envelope case, Mr & Mrs Sheepshanks.
Silver fish knife and fork, Mrs Naghten
Silver salt cellars, the Rev H. and Mrs Trotter
Silver napkin rings, Mr Edward Gillett.
Silver muffineer and waitbuckle, Mr Sholto Murray.
Silver-topped scent bottle, Lord Frederick Fitzgerald.
Silver fruit basket, Major Chalmer, 60th Rifles.
Gold bangle, the Misses Douglas.
Pair of silver revolving entrée dishes, Major & Mrs Murray.
Silver Apostle dessert spoons and dessert knives and forks, Mr and Mrs Grant.
Breakfast service and china ornaments, Lady Edwardes.
Card tray, Colonel and Mrs Grimston.
Glass rose bowl, Mrs Grimston.
Silver salt cellars, Mr and Mrs Douglas Murray.
Cut glass scent bottle with gold top, Captain and Mrs Eccles.
Gold inlaid tea service, Colonel Murray, 28th Regiment.
Silver pencil and pen case, Mr Vernon Eccles, Rifle Brigade.
Entrée dish, Major Douglas, 52nd Light Infantry.
Plush photo-book and cruet frame, Mr Angus Douglas, R.N.
Chippendale corner bracket and mirror, Mr C.C. Douglas, the Cameronians.
Silver pepper pots, Mr and Mrs William Gillett.
Cut glass scent bottles, the Misses Beadon.
Drawing room clock, Mr and Mrs H Sholto Douglas.
White Dresden china vase, Mr and Mrs Mordaunt.
Russian leather reticule, Mrs Blathwayt.
Glass water jug and goblets, Captain Saunderson.
Worcester china ornament, Colonel Skipwith.
Cuttack silver bracelet, Mr F.M.S. Douglas.
Silver bangle, Mr Ernest Blunt, R.E.
Case of silver napkin rings, the servants at Moorlands.
Silver flask, the servants at Harefield.
Toilet set in crocket, Mrs Balchin.
Handpainted toilet set, Miss Ethel Douglas.
Pair of china vases with raised flowers, the Misses Davison.
China bowl, Admiral and Mrs Coote.
Brass mounted mirror, Mr and Miss Coote.
Metal fancy inkstand, Mrs Willis Fleming.
Silver beaker and glass vase, Mr and Mrs Steuart Macnaghten.
Pair of china vases, Mr Frank Murray.
Silver tea kettle, Miss Gregory Smith (i.e.Constance Smith).
Picture and glass vase, General and Mrs Raymond.
Fancy table. Mr and Mrs Jackson.
Silver muffineers Mr and Mrs Holland.
Set of silver buttons, Mrs Herbert Norman.
Glass flower vases, Mrs Davison.
Pheasant-eye glass bowl, Canon Murray;  and numerous others.

The connection between the Douglases and all those Murrays is that one of Captain H Sholto Douglas'(father of the bridge)  sisters, Marianne, married the Rev. George William Murray;  Mr Sholto Murray and Mr Frank Murray are two of their sons. Miss Constance Smith is a grand daughter of theirs.  Another of Captain H's sisters, Helen Douglas, married Rev. Thomas Boyles Murray, and their offspring include Mr & Mrs Douglas Murray,  Colonel Murray.  
Canon Murray mentioned at the end of the list of gifters is (I think) George William Murray, the husband of Marianne Douglas.

Lady Edwardes (recte Edwards) was the elder sister, Maria, of William’s late mother and the wife of Sir Henry Edwards bt, MP.
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