To not want to send dd/have dd friends.

[Pretry]

My dd is 7 and has a group of four best friends. One lives about 10 miles away near school and the other two in our village. They are in the same class at school and all attend the same gymnastics club which takes up far too much a lot of her free time.
Aibu to not want to see the other children or to send my dd to them for the few hours/days they are not at school or gym? . My dd is not fussed as she likes playing with her little sister but the pressure from the two other families is endless.

Play dates are hard work. Once they start it is hard to curve them and hard not to reciprocate.
Don't do it!

Why don't you have to have one of the kids around at yours? It seems like a good way to develop friendships. I know you think they see each other all the time at school/gym but having some time playing properly is different. We quite enjoy having some of our DD's friends around (she's 7 too). I will agree it's a bit harder the other way round (sending her there) as I have 2 younger kids so the oldest is the easiest and helps with the siblings LOL but we do send her once in a while as she enjoys it!

How are play date hard work? I just stick to what we would normally do but with an extra kid lol sometimes it's a bit more tiring than having just our kids. Sometimes it's easy as they all entertain each other. I found play dates are becoming easier and easier with my oldest. When she was 5yrs old it was different as play dates involved the other parents too etc.

How much time is gymnastics?

If your Dd isn't bothered and actually likes sister time, there's your excuse.

"Sorry, the girls like their time together as Dd1 is so busy the rest of the time".

I wouldn't have them after school, but I don't think it's unreasonable for them to spend time together sometimes at weekends, half terms or school holidays.