I've sort of been where you are, as I was left with a baby and a toddler and my toddler was autistic. It is really hard, but it feels like you are being very passive at the moment, probably because you are over-whelmed and depressed.
You need to get clear in your mind what you want here.
Do you want to reconcile with your husband? It sounds as though you are really undecided, if you have had sex with him since separating and you are aggrieved that he is on a dating website. If you do, then you and he need to try and take steps to do that and have a proper discussion with him about how that could happen or if he wants that to happen.
You need to get some kind of shared parenting in place. Can you have a conversation with your husband about this and if he is too pathetic a human being to do it by himself, can you ask him to rope in a grandparent or sibling to help him?
I think you should consider some counselling. You say you don't want a 25 year old or a 50 year old telling you what to do or not understanding what you are going through, but that's not how counselling works. A counsellor will just facilitate you to think about things yourself.
How did your separation come about?