Anne is right -- you could talk about a "ramp up" timeframe for visiting H when he is in town.
- This month, 1 night.
- Next month, 2 nights.
- Next month 3 nights.
- Next month 3 nights, one of them a sleepover.
- Next month 3 nights, 2 of them a sleepover.
- Next month 3 nights, 3 of them a sleeopver.
Or whatever pattern/speed you come to agreement on. But this has to move forward.
It is not fair to say ok to poly and then deny you the space / time to have your other relationships IN because of internal fears.
Feeling weird about bringing it up is NOT a reason not to care for your partner's health and well-being. That's not being a good partner to your person.
I do not love having the doctor talk with DH. He will happily squirm his way out of check ups and dental appointments if I let him. For his long term health? That's not good.
It used to piss me off that I had to nag. He complained that I nag. I ask him what other choice do I have then when he plays avoidy? Does it respect my time and energy when I have to set up and cancel things for him? Should I leave him because he causes me pain and worry because he won't care for his own body bucket healths? He got sober about it and owned that YES! YES! He is afraid of doctors and dentists! And I said "That is fine. I can come with, I can hold your hand, I can do the appointment setting. I can even do the talking. But the GOING? You MUST go!"
So for his easy ones he does go on his own. For his others ones I've shown up and gone with. He gets extra support to get through it. I get to not nag. Cupcakes for all.
But without first speaking up you are not going to find out WHY he is foot dragging on the healthcare either. Does he have a doc/dentist phobia thing like my DH? In addition to the poor self esteem?