The attention seeking behaviour you describe is usually rooted in insecurity.
Do the girls have one set of boundaries, rules and expectations at their mum's house, but a completely different (nonexistent?) set of rules at their dad's? That will actually contribute massively to feelings of insecurity.
It's one thing to have slightly different expectations between houses. Like, maybe at mum's you need to keep your bedroom tidy, and at dad's, the bedroom isn't a priority but you need to help dry the dishes instead. In my limited experience, that's a reasonable adjustment for a child to make.
But children really do thrive on consistency and routine. If your DH has them at his house on a regular basis, then keeping up a similar routine to what they have at their mum's will help them feel more settled. My DH and his ex did have slightly different expectations of DSD when she was young. But bedtime was the same between houses. Other big things like eating a balanced diet, doing homework, manners, and how discipline was enacted were pretty consistent too.
I think it can also be normal for a parent (maybe especially a dad) to believe they have a favourite child. But I think that in practice, that just means there's a child the parent has more in common with. IMO, it's normal to realise you have more in common with one child than another. But that should be motivation to get to know the other child better, and maintaining balance. Where is your DH's motivation to spend some quality 1:1 time with his younger daughter?
When it comes to 10 year olds taking things too far and being a bit rude with questions ... sometimes at that age they can just be really socially awkward. They're trying to run with the grownups and often getting it all wrong. Ask me sometime about my 9 year-old DD trying to be sarcastic. 😬
Best thing that's worked for me during those moments is to gently but firmly explain how the behaviour is awkward, and how you're feeling about it. Or, if you're beyond that (we all have days when we're beyond that), a polite but firm: "I'm done now. No more questions."
Why do divorced dads spoil their kids? The one I knew IRL was terrified that his kids would refuse to see him if he started enforcing any boundaries. I knew a divorced mum who expressed feeling in a similar position with her DC when they were younger. It's anxiety talking though, not reality. Kids just want to love their parents, and know for sure that their parents love them back.
If you're looking for another good book, I highly recommend How To Talk So Kids Will Listen, And Listen So Kids Will Talk. An oldie but goodie. Set me on a better path with my own DSD, and set my DH on a better path with her too.