So don't let go of the balance.
A sponsor is a human being and has their own subjective view.
This person may not understand how exercise really helps mentally with coping during difficult times.
My husband isn't an exerciser, and frankly, he doesn't really "get" why I need to work out,
but he's been married to me long enough to know that it works.
He will even suggest I go when I'm getting maxed out emotionally--
Dealing with the stress of single-parenting and divorce sounds like
a really good reason to spin so long as you are also getting support for not drinking.
Which you are.
Trust your instincts about your needs. You know you best.
Hugs during this difficult time