How do you deal with splitting from someone after 10 years?

How am I supposed to deal with this? I've just kicked my husband out for cheating, we've been together for 10 years, married for nearly 3 and have young children. It's not the 1st time he's been unfaithful and I just can't take any more of it no matter how much he says he won't do it again I've heard it all before. He never really made an effort for me, just grovelled and said he was sorry when I caught him out. Surely I'm entitled to have scruples and say enough is enough? Why is it so hard then to know I'm doing what I need to do? I can't take anymore heartache I've had enough, anyone else been through this? Have I done the wrong thing?