I know it's hard being in a new area, trying to meet new people, balance all areas of life....
Just for reference, my daughter is now 20 months old, and is also a very attached girl.
Personally, I wouldn't leave my 11 months old at a gym or church nursery. In my experience (and your child may be different) my daughter simply wasn't ready. She either sits with us in church or her dad or I play with her in the nursery or outside if she gets fussy in the service.
Dh and I take turns going to the gym, too. That means that we each only get about 3 times per week right now, but we try to do more family workouts like walking with Emmaline in the backpack or sling, or even all dancing to music in the living room. It's not the same as a power workout at the gym, but sometimes it's the best we can do, lol.
As for the staff rolling their eyes or making comments, I would worry that they wouldn't
page me if my daughter needed me or was fussy. If they are doing those things, it seems as though they think you're being excessive or silly when you say you don't want your son to fuss or be scared (which you're not, you're being a responsible, caring parent). If they think you're being too protective or whatever, what are the odds they'll actually page you to come comfort him? That would worry me.
I wouldn't "make" him do it.
I totally understand about missing time together with your dh. We used to workout every day together, and I miss it too. But these baby months are almost over, toddlerhood will fly bye, and then you'll have more flexibility. It won't be like this forever. Emmaline is just 20 months, and sometimes I look at her and think "Where did all this time go???"
Maybe you could find a mommy and me swim class? LLL meetings almost always encourage and welcome children to attend, and it's a great place to meet AP moms. Get a good backpack, and hit some trails or nature areas as a family.
Edited to add: A couple of weeks ago, dh did take Emmaline to the nursery and she saw a little buddy of hers and said, "Bye Daddy" and he sort of disappeared around the corner for a bit. He peeked back in a few times, and she was just fine. So, he came back up for the last 5 or 10 minutes of church. So it will happen, lol.
Good luck to you~