There is a birth record on FreeBMD for Louisa Kathleen Coretts Trotter for Q1 of 1863 which looks believable.
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1901 census:

Research Log Surname Forename Age Relation  Occupation  Birth Place

Haldane John S 40 Head  University Lecturer MD Not in practice  Scotland
Haldane Louisa K 38 Wife London
Haldane John B S 8 Son Oxford, Oxfordshire
Haldane Minnie M 3 Daughter Scotland
Mangill Robert H 20 Nephew Doctor Of Medicine Surgeon  Scotland
Egerton Guy W 9 Nephew London
Egerton Arthur E 7 Nephew London
Bannell Mary K 27 Servant Table Maid Domestic   Ireland
Pinnell Ada U 20 Servant Housemaid Domestic Dorchester, Oxfordshire
Hire Florence E 19 Servant Cook Domestic Oxford, Oxfordshire
Perren Charlotte 24 Servant Nurse Domestic Henley, Oxfordshire

Ref: RG13/1381/~F37

Address: 4 St Margarets Road
Parish: Oxford St. Giles
Registration District: Headington
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On 15th Nov 1906 she appears to hav e matriculated her arms as ‘Trotter of Haldane’, as in the Ordinary of Arms, Vol II.  However the Scotland’s people site does not show this matriculation but does show the apparently identical one for her husband; I have downloaded this as it give the blazon for these complex arms in full, plus is gives a host of other relevant information in the full text in the Lyon Register.  The blazon is:

Quarterly,
1 and 4: Argent a saltire engrailed Sable (Haldane),
2: Argent a saltire between four roses Gules (Lennox),
3: Or a bend chequy Sable and Argent (Mentieth),
On the honour point a crescent Sable for difference,
The whole within a bordure Gules,
Over all on an escutcheon of pretence the following Ensigns Armorial:
Quarterly,
1 and 4: Argent a crescent Gules, on a chief indented Azure three mullets pierced of the field (Trotter),
2 and 3: Gules a lion rampant crowned Or armed and langued Azure charged on the shoulder with a crescent of the first (<owbray),
All within a bordure Gules for Trotter of Dreghorn.
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Within the text of the Lyon Regist is included that these Trotter arms were first granted in 1825 to “Sir Coutts Trotter bt, fourth surviving son of of the said Archibald Trotter of Castle and Bush with destination to the whole descendants of the said Archibald Trotter and Jane Moubray his wife.”

So the second Trotter quarter is clearly that of Moubray, or Mowbray and my earlier questions about where these Trotter arms came from can now be deleted.
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Being an enthusiastic genealogist and heraldist, she would have known that her father’s death meant that her husband was totally entitled to an inescutcheon of pretence.  It took from Feb 6, with due mourning interval, to 15th Nov of 1906 to arrange this.
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An Ordinary of Arms, pub Lyon Office 1977, Vol II, no 03866, pp. 257-8.

Their marriage:

Year Surname  Forename  Surname  Forename  District  City/    GROS
  (M) (M)      (F)   (F)            County/   Data
                        MR

1891 HALDANE   JOHN S TROTTER LOUISA K ST     EDINBURGH  685/01
                 GEORGE     CITY/     0458
                  MIDLOTHIAN
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