While her father was in England in the 1860s (he made a patent application), she was not recorded on either the 1861 or 1871 UK censuses.
________________

This 1870 census entry looks like her, though not with her family:

First name(s) Last name Gender Age Birth year  Birth place

Henry H Thomas Male 32 1838 New York
Josephine Thomas Female 32 1838 New York
Ann Thomas Female 54 1816 England
George A Thomas Male 27 1843 New York
Edwin M Thomas Male 2 1868 New York
Mary Sarony Female 16 1854 New York

Census details
First name(s) Mary
Last name Sarony
Gender Female
Age 16
Birth year 1854
Birth place New York
Race White
Residence Massachusetts, United States
City/township Boston, ward 12
County Suffolk
State Massachusetts
Record set US Census 1870
________________

In the 1901 census she was living at 50 Beaconsfield Rd, Twickenham, Mx with her husband and family, aged 42, born in New York, USA (British Subject).

A bit more information is emerging at the hands of Craig Rosenthal:  It is highly likely that she was the daughter of Napoleon Sarony, an extremely well known designer and photographer in the 19th century in the USA.  She definitely called herself ‘Mary Sarony’ at her marriage.

Further she and William had six children and the youngest was Leslie who, like his sister, was on the stage and took on the name of Sarony.  He is in the new ODNB.

Earlier censuses show that the family previously only used the surname of Fry (which could have been Frye and then misheard by the enumerator).  As yet there is no clue where the “Rawsthorne” bit came from, apart from raising the status of an artist!
______________________________________________________

In the 1911 census, she was said to have had 7 children, of whom 6 survived and one had died.

This looke like her death index, there are no other Frye deaths with the sole forename of Mary  from 1911 (when she was alive) to 1951 (when should would have been 95) and born around 1856 (in the 1911 census).

First name(s) MARY
Last name FRYE
Gender Female
Birth day -
Birth month -
Birth year 1855
Age 81
Death quarter 2
Death year 1936
District SURREY NORTH EASTERN
County Surrey
Volume 2A
Page 124
Country England
Record set England & Wales deaths 1837-2007
_________________

Their marriage index:

First name(s) WILLIAM HENRY
Last name FRY
Marriage quarter 4
Marriage year 1873
Registration month -
MarriageFinder™ WILLIAM HENRY FRY married
MARY SARONY
District SCARBOROUGH
District number -
County Yorkshire
Country England
Volume 9D
Page 684
Record set England & Wales marriages 1837-2008
__________________

The marriage from FamilySearch:

Name William Henry Fry
Birth Date 1852
Age 21
Spouse's Name Mary Sarony
Spouse's Birth Date 1854
Spouse's Age 19
Event Date 20 Nov 1873
Event Place York, England
________________

Sept 2020, TFPL: Their marriage register entry is foun d!  It includes:

Location:    The parish church of St Martin, Scarborough, Yorks
Cert No:     89
Date:        Nov 29 1873
                        His                         Hers
Name:           William Henry Fry            Mary Sarony
Age:            25                           19
Condition:      Bachelor                     Spinster
Job:            Artist                       -
Residence:      8 Martins Terrace            Sarony Square
Father’s name:  late William Henry Fry       Napoleon Sarony
Father’s job:   Dentis                       Photographer

Celebrant       J Moore Lister, Assistant Curate
Witnesses       O Sarony, Ce(?) Curtip

The witness O Sarony was the brother of Mary’s father Napoleon.
_________________