It looks like Betty may have gone by Bessie in earlier years.
1921 Los Angeles city directory Edwd J McDonough lab r751 Ottawa Bessie W McDonough clk r751 Ottawa
I can't find Edward and Bessie/Betty in the 1920 census.
This may be Bessie/Betty in 1910, although it shows her as being born in California. Alameda county is where Gwendolyn was born.
1910 United States Federal Census Oakland Ward 7, Alameda, California Thomas K Stwart 44 head m w md1 18yrs born SCT fborn SCT mborn SCT laborer Elizabeth Stwart 38 wife f w md1 5ch 5liv born SCT fborn SCT mborn SCT Christina Stwart 17 dau f w born CA fborn SCT mborn SCT waitress Isabella Stwart 13 dau f w born CA fborn SCT mborn SCT John Stwart 12 son m w born CA fborn SCT mborn SCT Bessie Stwart 9 dau f w born CA fborn SCT mborn SCT Samuel Stwart 8 son m w born CA fborn SCT mborn SCT
And this is likely Edward McDonough in the same census.
1910 United States Federal Census Oakland Ward 6, Alameda, California John P Beckerich 31 head m w md1 2yrs born NY fborn USA mborn USA laborer carpet cleaning Annie Beckerich 35 wife f w md2 6ch 4liv born MEX fborn MEX mborn CA Peter J Beckerich 1/12 son m w born CA fborn NY mborn MEX Edward Mcdonough 18 stepson m w born CA fborn NY mborn MEX elevator boy