Keep your mouth shut and put on a happy face until you get your ducks in a row.
Look up dopamine vs oxcytocin to understand what your wife is experiencing and why she will not quit.
Decide if you want out of the marriage or if you want to try reconciliation.
Do not move out. If there is a separate bedroom, move her shit into there, as she no longer should have the privilege of your bed.
Gather all the evidence you have on the affair, i.e. screen shots, forward emails to your account, etc, save it in a safe place and print out the most damning.
Find out everything you can about the POS trainer, like does he have a wife or girlfriend, her contact information, who he works for, etc.
Contact a lawyer and have divorce/separation papers drawn up. lawyer will tell you if infidelity matters in your divorce.
If you want out, have her severed (possibly at the gym) and inform the piece of shit personal trainer's employers what he is doing (using their place of business as a sexual recruiting tool.)
If you want to reconcile; the first step is No Contact with the POS Trainer, then expose her affair to family and friends, the POS trainer's employers and his wife/gf, continue marriage counseling, she gives you 24.7 access to her phone/computer/social media, she gives you all the details of the affair including a timeline of events.
When you confront her have the evidence and divorce papers in hand and give her option A, all of the above or option B, divorce.
Check out the chump lady for what real vs imitation remorse looks like, because without remorse (she has displayed none so far) reconciliation is impossible.
Good luck.
Also talk about marriage - coping with infidelity is an excellent resource for advice and continued support for whichever way you go.