The choice is your self esteem being crushed and always wondering what he is up to and modelling a bad relationship to your children or being alone and being worse off financially at least in the interim and maybe or maybe not finding a lovely man to build a life with. Or and it’s rare rebuilding and making it work, this is the hardest option. I’m much older than you and amongst myself and my friend's who I have known for up to 50 years, met first day of primary school, we have had every sort of permutation of how relationships work out.
A couple have been married to unfaithful bastards, a couple have been widowed, some divorces and some very happy marriages.
I for one would be out the door if an affair was revealed. When my friends DH had an affair she wanted to stay together, did the pick me dance, suggested counselling and would have done anything to preserve it, he left anyway. I’m can't be 100% sure how I would react but I would probably be one of those women that cuts the left sleeve off all their shirts and shits in his toolbox.
My Mums first DH was unfaithful, not my Father this was in the mid 1950’s, divorce was very uncommon back then but she just wasn’t having it and divorced him which was positively scandalous back then and was then a single parent of three for a while.
You will be ok, it may not feel like this is possible now but you will be. Sending many hugs and much love. My friend is two years down the line, when the decree absolute comes round we are burning her wedding veil and screaming like banshees, she wants to do this and I am her cheerleader in everything. Tell a trusted friend or relative in real life.