I feel for you. It’s hard to see a little child go through so much and then have to clean up the mess her mother is making. Kids lie and kids have accidents. And even if she is not having “accidents” you just need to go one like it’s no big deal. Make sure you remind her to go potty. Show her your love and tell her too. The other ladies have some very good point too.
When you are in new surrounding it can be scary. Maybe she’s and not sure what is next. Just be consistent. Being a little to lenient may not of been the best idea. Let her know what is expected of her and what will happen if she is unable to do that. Then the big thing is to follow through. Talk to her and find out what she is thinking. You may even want to go to the library and get some books on how to help her. As for her not asking for things or talking, I would just tell her she needs to use her words so you can help her or get her what she needs. Remember she is only four. Praise her for when she dose ask for something and does things right. You may want to set up some kind of reward for when she does thing correct like, uses manner without having to be asked, going potty on her own, telling the truth. You can to a simple things like an extra stoy before bed time or paint her toes or a $1 store treat. Or just some silly girly time. I know makeup spoke loud for my daughter. Even letting her put it on you would be fun.
As a child I stayed with my grandparents for 6 months every year. From 1st grade till 6th . I never knew when my mom was going to come and see me and when she did I would act out after she left. I didn’t know when she would be back. It was hard for me and it was hard on my grandparents. But I was scared and mad that she wouldn’t come when she said she would and afraid and sad that she didn’t take me with her. I never really new what was next. I guess my point would be to let her know what she can expect from you and her dad. And be consistent. Get a routine going.
Hope this helps some. I know it can be hard but just imagine what she will blossom into with all the love you're giving to help her grow.