Absolutely speak to an attorney. Having assets and children and being a man in the world today you have three strikes against you and the courts don't care, they'll take all your money in the name of the children and give it to her plus maybe alimony. An at fault divorce would do better to protect some of your assets.
Cheaters lie and they get better at it if they think they're getting away with it. Who says she doesn't skip the gym but show up first and leave her phone in a locker?
Trust is everything to a relationship and minimum I would not go for her ever going to that gym again while the OM is there. I'd also have her agree to having software installed on her phone. Doesn't stop her from getting a burn phone but just adds the extra layer.
Also remember this, unless you have evidence, if she's faced with her standard of living and a loss of some part of custody of children, (cheaters lie) she could paint you out to be a stalker who accuses her wrongly of infidelity and file a restraining order against you with both her and the children. What would a woman do to keep custody of her children and keep an income?
An good attorney could help you navigate this stuff. My state is a 1 party state meaning as long as 1 party consents you can record secretly. I have hours of recordings with my spouse discussing abuse (or lack therof) etc in how I treat her and the children. She doesn't know it and I had a friend ask her via text and they saved the conversation. I'm sure in court some of it could be thrown out for some crazy reason but I have enough that it would cause serious doubt with the judge especially since my wife was with a 2x convicted child molester.
Just remember that this woman is no longer the woman you have built a trust with. She is a completely different person and you either have to RE-LEARN to trust her and get to know the new woman or leave her.
IMHO cheating is like chicken blood to a dog. Once a dog tastes the blood it creates a thirst and desire thats almost impossible to quench.
Me: BS, 41 Her: WS, 35
4 Children
Married 19 yrs; DDay 3/2015
2nd DDay 4/2015 3rd DDay 5/2015, Breach of NC 4/2016, 9/2016, 10/2016, 12/2016
Started Real Reconciliation Feb/2017