I really feel for you!
This thing is part anxiety and part power struggle. Before giving up on the gym, I would try staying in there with her for a little while to get her started on coloring or playing or whatever. Try to do the old 'sneak out' once she is distracted. Bring a toy or lovey that she needs maybe.
Do you sometimes leave her with friends or family for and hour or so to get used to you not being there? I see that you are a working mom, so does she do well during the day without you? She might just really miss you! Plus she is contending with a new baby in the house...So many changes for a tiny one.
Hopefully the gym has familiar caregivers that she can start to get to know and trust.
If they come get you in five minutes, so be it. Calm her down, get her settled back in and put her back in care! Do they have a smaller child/baby area where she might feel more secure? Some kids are just really shy and are overwhelmed by older children or large spaces, loud noises...
Help her to understand that you will always be there if she really needs you, but that you are not at her beckon call either.
If this simply does not work for whatever reason, you can always take her and your new one for a stroller ride at a local park with trails, like Pflugerville Park, where you can burn several hundred calories and build muscle just by running or walking the paved trails. Pushing a kid is hard work!! Do you have a double stroller?
After a few weeks or so, give the gym another shot and keep working at it.
My little girl would cry and be upset when she was about 13 -14 months old at the gym, sometimes they would have to hold her and cuddle her to make it work and I was so thankful the ladies were willing to work with me like that.
I also explained that my girl loves to dance and watch cartoons like Dora and Blues Clues or the Wiggles with lots of music so the ladies would something on the TV and that really pacified her.
She quickly got to the point of making friends and trusting that I would be back soon. We really had to work at it. She is 2 now and LOVES going to the gym to see her little friends. She does not even blink an eye when I leave.
We can hire babysitters or leave her with friends so we can have an evening alone and it is SO NICE. The payoff has been huge to tough out those first 3 months.
Good luck!
S.