Seriously, why are you asking for adult replies on a kids board?
But to recap:
like almost everyone else has said you are overthinking this waaaaay too much.
What is there to think about:
rule of thumb number one: you should only do whatever it is you would do if your wife was there watching you. If you think she would be happy with you flirting with this woman then fine - if not - then don't do it.
Remember this woman works all day in the gym so she is most likely pretty bored and looking for a bit of action to take her away.
You made the equation - your wife and kid vs what, 10 minutes of banging away up against the stairmaster after gym closing?
There is no contest - but you have to be the judge.
Hell you don't have to be uncivil to get your point across to her. If she is any sort of woman she'll be fine with an honest explanation - I don't wish to nail you because I'm happily married (with a child). But thanks for the ego boost and if I was single I'd jump you in a second.
Leave it at that - if she still persists and things get messy invite your wife down to your gym and get the two of them to jelly wrestle for your affections - and as others have said make sure to film it and post it here.