Well I don't think having sex 1-4 times a day is unreasonable at all. OK, I don't think I could do 3-4 a DAY but...
My take on this is yes you're being selfish. Not that people aren't entitled to, I do my share of it but - You have only been seeing E a few weeks. I am sure E understands that your primary relationship is very important, and that Rider is struggling, so hopefully he will be understanding if for now you sometimes have to change plans to put your husband first.
It isn't fun to dial it back at first, but if you want Rider to feel important to you (and not feel more strongly that the marriage needs to be closed/or your relationship end) you will do that by SHOWING him with your actions. Having patience now will serve you very well in the long run.
"If every time Rider has a rough day I drop everything to come home or I stay home, he won’t be forced to overcome these hurdles. I want and need to help him but I don’t want to prolong the pain. I’m at a loss and I just want the drama to end and for things to be settled."
Ok, that is mean. Maybe you are just venting, but if that's how you feel, do you think he can't tell how pissy and impatient you feel towards him? How is that going to make him feel secure and safe in your marriage? It's better to focus on feeling gifted that he is trying to work on these feelings and the other things he does for you.
If you were in his place I am sure you'd like to be treated more lovingly than that statement there implies you might be treating him. Sadly lots of couples in the position you are can struggle months with this, so if you think he's just going to get over it already, you're probably in for a lot drama, but I think you need to realize that you're responsible for your share of it.
I don't know the whole back story or anything, so if I've made assumptions about anything I apologize in advance.
Happiness will never come to those who fail to appreciate what they already have.