You need to plan your life. Make all the dua you can but remember that Allah has made many provisions and ways with which a muslim should live a clean life.
I would suggest the following
For the present time, maybe 2 weeks or more, whatever your mental status is
1) Stop confronting him. He will continue to deny and will become desensitized and you will lose any little hold on the situation that you have. Ignore what he does, think of some activities to do while he is “on the internet” so that your mind is off him.
2) Keep all evidence that you have like credit card statements or tel numbers of dating services in a safe place.
3) Use this time to get a hold on your feelings. You need to come to a point where you are fully convinced of the reality, the problem is his and your whole family will not pay for it.
4) Become involved outside the house and make friends, get a support system going. Being lonely will make things very difficult for you. You can also look at counseling services in the area, maybe through your mosque. These days imams hear plenty of stories like these and they probably will know what works and doesn’t.
After you gain emotional distance and a support system and advice from a local imam etc, this is the time to confront him, tell his what he is doing is wrong because of the kids/your feelings/its haram/ etc etc and threaten to leave
If he refuses to change you will have to make a choice to stay and put up with this or leave (temporarily). Its bad but some people need a taste of what they lose if they don’t give up what they are doing. You may go to a relative or friend or be on your own. You need to be away for a susbstantial period and not go running back as soon as he says he is ready to change.
When he has had a time to reflect and when you are somewhat sure of the remorse, you agree to put things back to where they were on a set of conditions and he is on probation. If he is tempted to foul again, he knows by now that you won’t put up with any more trash.
Whatever you do, your aim should be to end this habit of his. Many times couples go through a cycle of ups and downs where one person apologises and is forgiven but then he/she goes and does it again. Believe me, years of your life can go away like this and somehow you will end up in a zone where to the pain will numb and all you feel is a disgust that you did not do better for yourself and your kids.
You can also cut the cord etc, but he can also go online in an internet café, in a friends house.