Member at one gym, training classes at another competitive gym...

I live in a small town. The gym I have membership at has childcare, which is huge for me as I have a 3 year old. They are highly competitive and have their eyes on everyone in there. I have been warned not to train with friends. Also, they don't like that I do a free class at my house on Sundays. They have approached me about training at their gym, but they don't pay well and treat employees poorly.

There is a much smaller one room gym two blocks away that an ex Fitness Director from my current gym started less than a year ago. She will take good care of me and allow me to teach a few classes there.

I am concerned if I do this my current gym is going to revoke my membership or harass me. Can they legally do this?