Kathleen made a few trips between England and New York. I didn't find a return when she made her last voyage in 1931.
Canada, Ocean Arrivals
Date of Arrival: 12 Sep 1920
Port of Arrival: Quebec
Kathleen Elizabeth Downer, Age 44, Female, Widowed, Occ: Cook, Intended Occupation: Domestic Employment, Born Oldbury, Staffs, British, Church of England, Object of coming to Canada: Domestic Work; Ever lived in Canada: No; Money in possession: $25.00, Can read and Write, By whom was passage paid: Employer, Intend to remain permanently in Canada: Yes, Destined to Employer (crossed out is Mr. Sherwood ?? Ottawa) and replaced with Mr. Gates, St. James St., London, Ont.
Nearest relative Kin country from whence passenger came: Son Walter F. Downer, 8 Morris Rd., Southampton
Canadian Passenger Lists
Port of Departure: Liverpool, England
Date of Arrival: 11 Sep 1920
Port of Arrival: Quebec
Ship: Megantic
Kathleen Elizabeth Downer, Age 44, Widow, Destination: London, Occ: Cook, Domestic, Church of England
Index to Alien Arrivals at Canadian Atlantic and Pacific Seaports, 1904-1944
Kathleen Downer, Age 44, Arrival Year: 1920, Arrival Country: USA
Philip was not traveling with Kathleen.
In 1923 Kathleen travels to Southampton and returns to New York:
UK Incoming Passenger Lists
Port of Departure: New York, New York, USA
Port of Arrival: Southampton, England
Ship: Leviathan
Arrival Date: 27 Oct 1923
Kathleen Downer, going to 37 Cranberry Avenue, Southampton, 3rd Class, Occ: Cook, Age 47, Country of last Permanent Residence: USA
UK, Outward Passenger Lists
Port of Departure: Southampton, England
Destination Port: New York, USA
Ship: Ohio, Shipping Lines: Royal Mail Steam Packet Co.
Date of Arrival: 9 Nov 1923
Kathleen Downer, Last UK Address: Dorset Ho?se, Cranbury Terr, So’ton, Occ: Chef, Age 47, Country intended for permanent address: USA
New York, Passenger Lists
Port of Departure: Southampton, England
Port of Arrival: New York, New York
Ship: Ohio
Arrival Date: 17 Nov 1923
Kathleen Downer, 47, Chef, Last Permanent Address: New York, USA, Contact: Brother, Mr. Alfred Wood, 32 Broad EyE. Stafford
In 1928 Kathleen makes another trip to Southampton and returns:
UK Incoming Passenger Lists
Port of Departure: New York, New York, USA
Port of Arrival: Southampton, England
Ship: Homeric, Shipping Line: White Star Dominion Line
Arrival Date: 13 July 1928
Kathleen Downer, Travelling to 47 Hatherly Rd., Southampton, Domestic, Ager 52
UK, Outward Passenger Lists
Port of Departure: Southampton, England
Destination Port: New York, USA
Ship: Majestic, White Star Line
Kathleen Downer, Last UK Address 47 Atherley Road, Southampton, Domestic
UK, Incoming Passenger Lists
Port of Departure: New York, New York, USA
Port of Arrival: Southampton, England
Ship: Berengaria
Arrival Date: 17 June 1931
Kathleen Downer, Traveling to Shirley, So’ton, Cook, Age 55, Last Permanent Address: USA
New York, New York, Index of Declarations of Intent, 1907-1924 (on ancestry.ca)
From Index only: Name: Kathleen Elizabeth Downer, Declaration Volume: 680, Page 54