The Chaplin Archive website identifies the woman on the left as Lita's mother, Lillian,
but it doesn't look like her to me (plus I doubt she would have her arm around Charlie)
On this day in 1928, Charlie's divorce from Lita became final. An interlocutory decree for divorce was actually granted on August 22nd, 1927, but the divorce did not become final for another year. Charlie finally agreed to a settlement when Lita's lawyers threatened to reveal the names of the "five prominent moving picture women," she alleged Charlie had slept with during their marriage. Lita had already visited Marion Davies, whose name was at the top of the list. Not wanting to involve the women in a scandal, Charlie conceded to a settlement: $825,000 (about 11 million in today's dollars) which included $100,000 trust funds for each of their sons.
Years later, Lita revealed the names of the other "prominent" women (besides Marion) mentioned in her divorce complaint: Edna Purviance, Claire Windsor, Pola Negri, and Peggy Hopkins Joyce. The problem with this list is that Charlie's relationship with these women had been long over by the time he married Lita. I believe this list was driven more by Lita's jealousy of Charlie's past relationships (with more mature and sophisticated women) than anything else. However, she had good reason to name Marion, whom Charlie evidently boinked in the servants' quarters of the Summit Drive house (he paid one of the cooks $5 to use their room) while Lita was upstairs giving birth to Sydney.*
*Lita Grey Chaplin, Wife Of The Life Of The Party, 1998