Sorry you're going through this. I don't know if it's something your husband would do, but there are other things he could be doing online that he doesn't want you to know about other than porn ie. "chatting" with other women. I would want to know what he's trying to keep secret. Myself, I would ask first, see if he would be upfront, and if he says nothing then might do the software to find out myself. You have to be sure with yourself that you truely want to know the answers, and decide what you'll do with the info that you get.
I have not had the most romantic marriage as well, but I think my husband is just incapable of it, he just doesn't see it. We're not very close anymore at all, I think difficult child's problems and how husband buries his head in his sand just put the seal on that. I did have a therapist once ask me if I did not feel that I deserved to be happy, that being with husband did not make me happy. Perhaps at some point I will leave, but I'm not in a rush 'cause I don't think some other guy would make me happy either, I've come to be happy within myself. I think that's a question you should ask yourself as well. I think you are a wonderful person who deserves to be happy. What I would say is that you should go to a therapist for yourself, as you say he won't go. Decide how YOU want your life to go, and what you need to do to get there. And go see your lawyer and anyone else you should be seeing to make sure you would be fine should a sudden separation happen. Your husband has already told you in 10 years it's over in his opinion, who knows if you or he might decide you don't have to wait that long. Yes, separation is hard on the kids, my parents were divorced. But they also see the tension and separation that is already between you two as well, I know we as kids saw it between our parents. I'm sorry, but in my opinion your husband has already separated from you, but wants to still live with you to maintain all the benefits, like cooking, cleaning, laundry, being with his kids everyday while you do all the work to care for the kids, someone to take care of him without any work on his part.
See the therapist, right now is probably not the best time to decide heavy stuff like this with Andre missing and that stress in your life. But think about what YOU need out of life, and that's a start for discussions with the doctor.
{{{{{HUGS}}}}}