I honestly really did trust him
I think he's proven that you can't. This is your lot with him - he'll always be on the lookout for other women, and he'll always lie to you about it.
I'd leave because he seems to have no respect for you, and he has had many chances to change and hasn't bothered. He has proven that he is a leopard that cannot change his spots, really.
You can stay, if you'd like, but for the sake of yourself and your children, you'd need to do it knowing that you can't trust him and that he'll probably be either talking to other women or looking for women. For some people, that's an acceptable compromise. You could ask him to be subtler so you don't see it wherever you go, but as he's been crap at keeping his secrets so far, I'm not sure he'd be capable of it.
If you do leave, prepare yourself for him to be shocked - he'll be expecting you to forgive and forget like you've done in the past. He'll probably cry a bit - they'll likely be genuine tears, but he'll be crying that he's been caught, not that he's sorry. He'll probably promise that he'll change, and when that doesn't work, he'll get bitter and accusatory. Remember that he's had plenty of chances to change, and so far, he hasn't bothered. He won't.
I am sorry 
Is he around today or do you have some space?