I'm sorry your husband has left you after a marriage that has lasted this long. So he has a pattern of leaving and, then, wanting back. In the past, that seemed better to you than terminating the marriage. Would you be willing to take him back again, if he made that turn-around again? What is the reason for the contact once a week, if you can talk about that? Are the adult children there by design, as witnesses or for support, or protection? Do you feel supported by your children?

I've never been married, but I'm in a 32 year relation with my sig. other. So there's a lot I don't know, but my understanding is that dissolving a marriage can have financial aspects that need to be treated with care. I would be concerned about you not having any legal counsel. Ideally, you and your husband should each see your own attorneys. After 38 years, you may have a claim on his source of income or future pension. Be careful that you don't sign away rights that you shouldn't sign away. Not having an attorney can often be more expensive than having one. There's no need to rush into a divorce.

Right now, the worse thing is the emotional pain. If you were to write a letter, would that be to your husband? Are there things you feel a need to express to him?

With your husband having a history of leaving and returning, my guess is that he may be someone who never fully matured. I think not chasing him is a good idea. There is nothing wrong with just not doing anything for a while. I hope you have some family or friends that you can spend part of your time with. Too much time alone is not good.