It all depends what the kids want, if she is loving and supportive towards them and you think you can get over it and still live a life yes its fine. If you can't handle it and don't think you can get over it then its time to say goodbye. If shes infront of you texting a guy or in her own home doesn't really change anything besides you having to see it.
I'd stay for children but thats me. If my kids were upset about mommy then I'd make sure she cleans up her act and at least hides it from the kids. Children are impressionable being raised in a broken home is tough. I wouldn't want my kids to go through it. Kids need parents. Marriage is one thing but sharing life is another. Sometimes things happen and unfortunately marriage doesn't always work out but in the end you have no choice but to do whats best for your children.

I don't get it why doesn't anyone message me lol
Is it something on my profile?