This is what I wanted to say. It depends on if you want to do it. You DD doesn't *need* to do tumbling. But it's a nice thing to do. Our kids also do things like that but they would be cut if we couldn't afford it or were trying to cut back more.
I guess what it comes down to is if you and DH really want to cut the budget. How much convenience you want, how much comfort you want etc. Everyones level is different. When I look at your budget I seen many things that can be cut. But thats me, not you. AND your Dh needs to be on board too. The other reality is your wont be on your parents insurance forever so I would look at a budget with numbers where my household would be paying all the costs.
When my DS was 2 yrs old we lived at the library. We did story time several times a week. Sometimes we went to different branches/library locations for a bit of variety. There is no reason you cant go to the park when its cold outside. Obviously if the playland is buried in snow that makes things difficult but just cold shouldnt be a problem. Get a jacket, sweater, hat etc.
For socializtion DS and I joined a mommy group and for a few dollars a month we went to playgroup at someones house. The scheudle rotated.
You and DH need to really want to cut the budget. You both need to give things up. Maybe internet stays but then everyone gets at home haircuts. (just an example).