Sounds fantastic what you have planned.
I would forget legoland and go to the Kennedy space centre (especially if this is the only time you’re doing this kind of holiday etc)
As another poster mentioned go for when the parks open, and make the most of the day.
You won’t need a few days at universal. You can get a joint ticket for universal and islands of adventure I’d say a day at each. If you are staying at hard rock for a night you could tie it in in those days.
For Disney I would say full day at Disney magic kingdom itself is ample. Get there for when it opens, fireworks are good to! Go for fast track passes as the queue times are very excessive for some of the rides. A water park I wouldn’t give a full day to, universal also have one now so depends on whether you want Disney or not. Maybe later morning to late afternoon.
I would say 3 days is enough for universal, islands of adventure and magic kingdom. Half day for water park and full day for kenndedy space centre. If you do go there see if there’s any launches happening whilst you’re there and tie it in.
I’ve purchased on the gate, pre purchased online I’ve also used guest services. I’ve never actually purchased tickets from a UK seller.
I would have a good look on their official websites (universal and Disney) see what options work best for you for how you want to work it and then you know what to look for from other vendors and find the best price. It is expensive for park tickets, and if you felt budget was stretched too much you could maybe get a park hopper ticket from universal where it gives you access to both their parks in one day. But you would have to be super organised with what you wanted to do and see.
With Disney, the girls will love it it’s not overly princess and there’s so much for them to enjoy (and the adults to)