This is pretty much how every single homework experience has gone since she started getting homework in kindergarten. Somehow, the prospect of homework liquefies my daughter's body and she melts into a puddle onto the floor.
Some kids need time to transition back home after a long day at school. Perhaps they need to eat or burn off a little energy before doing homework. Others might be more successful doing homework immediately before other things get in the way.
Group projects have always been maybe the worst thing ever about school, aside from actually having to study. You're forced to work with people you may not like or work well with, or who might not always put forth effort in the group.