The thing about bereavement is you need to give yourself time to grieve properly. I remember when my mother died, I was a mess for months. I took a full year to 'get over it'. Of course you never are fully over it. So even forgetting about your husband, you are going to need to think about yourself. Please don't forget this. You have a lot of difficulties and this is why you are going to need to be really careful. Your children need to be loved too. You will have to get to know this new husband of yours slowly but surely. He is the father of your children, and you understandably will want to start a new relationship with him if you can save your marriage. But he isn't the same person who just died, and he never can be. He needs to studiously start to try to solve his really quite serious illness. Beating PMO and sex addiction needs to be handled like a military operation: he has to engage with you in meticulous planning, and take a holistic approach. His whole life has to change right now. It is an illness, he must understand this. Our society unfortunately dosnt treat this anywhere like with the seriousness it deserves. It isn't just cheating. I wish you well. Be proud of yourself - you are clearly an incredible person.