I'm glad to have met you in the cafe. I'm sorry that things are tough for you right now.
You have some wonderful advice here from kind and caring people.
I suggest checking your list and perhaps writing more. Often when one part of our lives stops going so well we go back and reevaluate everything so it can be a really confusing time. There is some information about this if you search up Maslows basic needs.
What I find helps is a list of what you want in life, in your relationship, your goals both short and long term. Then look at what you can and can't control on that list to make it happen. Once you have this I find things get clearer on what you really need and how those things are or can be met.
An example might be: I need friends. What you can't control is that your partner is not comfortable with people at the house. What you can control is to arrange to meet them out or ask your partner to go out elsewhere when you want them over. Perhaps you can do this when he goes to his kids for dinner?
Sadly you can't control how the kids behave with not inviting you but you can choose how to spend that time. I have a friend who immensely dislikes her partner's daughter for absolutely no reason. The way she talks shows that she just doesn't want to share him. You never know, your partner's kids may be the same as irrational as it is, try not to take it personally.
It is nice to feel needed by someone and loved especially if you are unwell yourself and are needing that security and comfort. You both seem to fulfill some needs for each other but perhaps are questioning is it enough.
I'd have a go at writing it all. Perhaps that can then be something you can use to talk through with him. I think Lyn has an excellent point about men not always knowing how serious it can be and it coming as a shock when the partner leaves. I have been through that too in my past.
I also have a chronic tension headache that is constant so I empathise with your current pain and limitations on what you can do if you ever want to talk about it.