Won't go into the details of my situation but I think you're already doing the best you can do. Spend a little extra time you have with the child to re-affirm her worth and self-esteem that does not directly contradict or target her mother. Anything more than that could back-fire and you will be shut-off from the kid. So just get-in where you fit-in and do your best to make a smaller contribution in bigging her up as much as possible.

The only way you could go a bit further....but there's a risk....is to use some subtlety and go out of your way to praise the child in the mother's presence. 'Damn you're daughter is such a fine young lady and so well-balanced. It's clear you guys have done such a good job raising her'. That COULD work to disarm the mother's criticism (albeit temporarily) during that particular encounter. It's effectiveness would depend on your ability to dole out nuanced back-handed compliments and also how the mother's particular personality might react to such tactics. Would she be smart enough to figure out what you're doing? If so...is she aggressive enough to call you out on it?

It kinda works for me with the young lady and mother that I experience this with. And when the successes and accomplishments of the young lady get tied to the mother's ability to child-rear....she kinda gets off the verbal criticism because it becomes associated with her not being a good mother. It involves a little phoniness and it makes me cringe to praise this mother that is clearly too verbally abusive....but it does kinda change the dynamic for the rest of my visit. And it's fun to big-up the daughter in a way which the mother can only contradict if she wants to criticize her own parenting. So if you think you can get away with manipulating the conversation to push in that direction....it might be worth a try.

Alot of kids who grew up under abuse look back on a particular uncle or aunt or mentor or teacher who made an effort to big them up and that sometimes sets the stage for a very close relationship in the future (ie My aunt was always there for me when Mom went off the deep end). So even though it might FEEL like you should be doing more...take comfort in that what you're doing is already of benefit and very important.