I think you make a really good point about Amy being in fangirl mode but I'm not so sure about the power imbalance. Sure, Tom is more well-known than her but I think it's important to remember that Gi has 100% taken advantage of his name to bolster her own endeavours. Her first book, Billy & Me (I think that's the name) was essentially a story about a woman dating a pop star, it was practically her autobiography and the fact that it was vaguely marketed in that way is what helped it become a bestseller (my housemate works in publishing and her company currently represents Gi and she's pretty much confirmed this). Then the baby stuff, she has made a career for herself using her - but also his - kids and his platform. So I don't think she's just Tom from McFly's wife anymore and hasn't been for a long time.
It's a similar story with Carrie - she rode on her brother's success for a while too, heck, he even paid for her drama schooling because she didn't get into the school he went to. I think Tom has gotten so used to people riding off of his success without showing much appreciation for the work he does that having someone like Amy, who is successful in her own right, fan girl over him must make him feel like a new person.
This definitely sounds like I'm sticking up for Tom which I'm not, he's making a fool of Gi but I get sucked into this kind of stuff so it's just a bit of fun theorising!