Am I wrong to ask for the account closed?

I know there are so many ?s about facebook and twitter that its ridiculous but I need some advice. For the past lets just say a year (even though its been a bit longer) I have seen several times on my spouse's twiiter where he says things like "let me jus put the head in" or "damn you got some sexy *** lips" or even "meet me in 20 minutes (in response to a woman's sexual twit)" I told him a year ago that it makes really uncomfortable & it hurts to see him talking to other women this way not to mention if our children read it. He has promised at the very least 5 times but continues to do it. I found (yes I was looking through his twitter when he forgot it open) a private conversation with one of the women that i think he met a year ago (there has been several others too but this particular private convo was last week) and in it he is describing a sexual dream and telling her he wants to "go down" on her. I looked at the timestamp and it was an hour after I had seen something just like this and he promised and actually begged to make it right and be a better husband. We have 3 children and I have been far from a saint in our marriage but I am really trying but my confidence & trust in him is shot! I asked for him to delete his twitter since that has been the biggest (not only) source of our issues, as a show of his seriousness. Do you think it even matters to have it deleted or do you think I'm unreasonable, I am very devastated because to me these conversation weren't playful they were hurtful and the fact that they went on after they shouldn't adds insult to injury. Please help...other than just divorce (I know that is an option).