Your eldest is 10 so is well old enough to understand basic manners in a household.
If she is pushing back / back chatting & rebelling is it possible to try approaching her by letting her know you have done your very best to create a harmonious, safe & happy environment for all of you to be a loving respectful family.
I would tell her that I missed her dearly when she was at her dad’s but that you don’t miss her behaviour while she’s here.
Also maybe approaching it that leaving messes everywhere is like a little kid - it’s immature, she is double digits now & a proper young Woman now. What would she do if you decided to not clean up, or shop, or cook, or clothe your girls?
She needs to see for herself that her actions are making her own home life negative for herself - with you having to rouse on her to clean up etc.
Maybe if funds allow provide her with an incentive to be tidy ? Like every month if all her chores are done & room is clean you will buy her a treat which is something she can decorate her room at yours with?
So every time she achieves that she gets to improve her little oasis at yours & will appreciate you more?
Don’t have kids myself so it’s just a thought
You sound like you’re doing the best you can & have done so well to get away from a toxic relationship.
The only thing you can do when someone (ie your ex) is bad mouthing you is to keep living your life & eventually people will realise that your actions don’t match their words.