Anyone got any advice

So me and my ex husband divorced 2 years ago nearly never went to court or anything just mutually divorced we got a daughter together she will be 10 in September he was abroad most of the last couple years he saw her here and there when he came she goes sometimes at holidays but not always I don’t ask for any maintenance or nothing we are both remarried he married abroad but now I’ve moved to another city I always made her keep in touch with his family even when he was abroad even now I make her call him all the time and keep in touch etc but she doesn’t like to stay anywhere without me so when she goes there she wants to come back the next day literally I do explain to her to spend time with her dad etc but the time apart has caused a distance between them

He generally asked me saying can he put my daughters name in his council house with him and his family I said no he said okay

But I’m just a paranoid person and pregnancy doesn’t help I’m thinking what if he tries to do it behind my back or tries something to take her away from me or something

I mean she’s really happy here goes to school made new friends really gets on with my partner etc

Does anyone know if his got much power to do anything?

He is on her birth certificate and he is her biological father

I do trust him just not his mum and family feel like they will try to be sneaky about something

Any advice would be appreciated just to put my mind at ease