Ds1 (nearly 7 years old) has hypotonia and hypermobility. He couldn't even get himself to sitting at 15 months old, but with physio was walking by 23 months. He did do a local gym class from age 3 to 5-and-a-bit - lots of bear walking, wiggling along the floor like a snake, etc, and didn't stand out too much as the age range was quite large. The 5-7 year olds' class was a bit more of an issue, as there were some activities he clearly had difficulty with - his shoulder girdle is particularly weak, so hand stands, even with teacher support, were quite risky, given that his arms could just give way under him! Also, swinging from bars, as his shoulders are so hypermobile and weak we'd been advised not to really do swinging activities with him for fear of dislocating something... Most of the class was still fine, as it was mostly still floor activities and fun, but the more structured side was where he stood out a bit and so he chose to give up. It sounds as though your dd isn't as extreme as ds1 (who actually has a diagnosis of Ehlers Danlos syndrome, hypermobility type), so she may be OK with it.
Swimming is supposed to be the best exercise, as it exercises all muscles without risking damaging joints (all hypotonic people are more at risk of bending their joints the wrong way, which is why hypermobility often goes along with hypotonia).
As for hand activities, I've found nothing better than the piano for helping with ds's hands - he hated lego, playdough, colouring in and the other things he was supposed to be enjoying playing with when he was little, but he enjoys playing the piano.
Oh, and we perservered with playgrounds and soft play areas, pushing his bottom up ramps if necessary when he was younger, and really encouraging him to climb and explore, and he's actually pretty good on playground equipment these days and really enjoys it.
Shoe inserts are really helping ds1, too. When very little he had piedro boots, then a few years without extra support, but having the inserts has really helped in the last few months - his running style is less flat, now, and his ankles are no longer scraping the floor!!!!! He also has lots of exercises from the physio which are helping.