DD and dominating friend - how do I teach her to be her own person

[Vinegar]

DD is 5 and in reception. She and girl X have been friends for 2 years. I am friends with her mum and they are in the same class in school.
Recently Dh and I have noticed that dd is totally dominated by girl X. Girl X is not very sporty and is scared of animals. She will not attempt things like going on high slides/climbing frames. When they are playing together dd seems to follow girl X's lead, even though dd is very sporty and enjoys doing these sorts of activities. However, girl X deems them silly/boring and dd will then say the same.
Girl X is also very good at talking herself up, saying she can do things when she can't. She is very loud and can be horrible to other children. When she is with girl X, dd seems to change personality and follow her lead. She does not want dd to play with anyone else and will often push in and pull dd away from other children. She always wants dd to play her games and will often cheat so she wins.
I know girl X is actually an insecure child(her mum is very shouty and seems to favour her brother), however, Dh and I would like dd to stand up for herself. I don't want dd to stop being friends with girl X, just to be able to voice her own opinions and not be such a follower. I know as they get older there will be other children like girl X, so we want dd to learn to be strong enough to deal with children like this or it could eventually turn into bullying.
Does anyone know how to deal with a situation like this?
DD is well liked in her class and does have other friends. I don't think the teacher sees how dominating girl X can be, as girl X is extremely eager to please the teacher and can often show a completely different side to her when adults are around.
I do feel a bit guilty in that as I am friends with girl X's mum, they have spent alot of time outside school together and maybe this has contributed to the behaviour.
Girl X's mum would not tolerate girl X being bossy, however I(and dh) have observed this behaviour when we are around the two of them and by what dd tells us.
When we ask dd why she listens to girl X, she says because girl X "knows everything" or that sometimes girl X shouts at her. She enjoys girl X's company(will ask for her to come home to play)and is maybe flattered by her attention.
Sorry this is really long - thanks for reading if you have got this far!
Dh and I have talked to dd, but I don't know if there is anything else that we can do.

I have had the same problem with DS1, who is now 6. He became best friends with a boy in Reception who was very overbearing, and DS1 who is very easy going was totally dominated. The friend always seemed to be putting DS1 down, for example if DS1 said he had a book on Dinosaurs, the friend always had a bigger or better one etc, always said he was able to do whatever it was better.

I know it is difficult if you are good friends with the mum, but I would just try to encourage other friendships a bit more, maybe arrange playdates that don't involve the bossy friend, so that your DD has a chance to be herself. It doesn't mean she has to stop being friends with Girl X, but if she sees how others play she might be able to assert herself a bit. Particularly if its a new friend who is keen on the things that Girl X is not keen on, like the sporty, adventurous stuff.

Thanks Basement bear. Maybe a bit of a break over the summer holidays will do some good. It's hard arranging playdates with other children from her class, as some live a bit far from the school and others often don't seem as interested in meeting up(the children are, but too much of an effort for the parents).
Just have to see how it goes when she is in Year 1.