If I was you OP I wouldn't kick him out , I'm sorry I'm inclined to believe what he says, I think if there was more to it there would be more texts on the phone bill.
If it was kiss or sex , well to me it wouldn't matter, a betrayal is a betrayal so what exactly happened I wouldn't care about.
That aside I still wouldn't end my marriage over it especially because there is children. I would be very upset and my husband would need to do a lot of grovelling but I do believe people make mistakes and do learn from them.
I think your husband will be terrified he has lost his whole world, his wife, children, job over a stupid encounter or two and will hopefully learn from it
I think marriage is hard, and we have some many hurdles and difficult times but people can move past things like this
Once I could forgive, if it happened again he would be gone.
I've been cheated on by a long term partner in the past and I did forgive him and move forward as it happened later down the line we decided we weren't for each other and went our separate ways, but we have remained friends , he is a good man and even to this day he knows he made a mistake and says if he could turn the clock back he would and he says he will never hurt another woman in that way and I believe him
I'm happily married to another man now and if this was happening to me and him , I would forgive him and give our marriage another shot
Don't do anything hastily and to be honest I'd not listen to advice from stranger on the Internet about something as important as leaving a marriage, listen to people who know you, know your husband and know your life
Good luck I'm sure things will work out for you.