Re (from MelinaJ
"I did ask Dan to simply let me compromise by just seeing Joe once per month in that study period but he objects to that."
Hmmm. Still it sounds to me like a reasonable compromise and so, at the moment my vote would be to tell Dan, "Well, I'm afraid I'm going to see Joe once per month during the study period. I hope you'll be willing to accept that compromise, but with or without your blessing it's what I intend to do."
The only other way to look at it is this. Is your relationship with Dan more important to you than your relationship with Joe? and is Dan going to break up with you if you fail to adhere to his wishes? If the answers are yes and yes, then you should probably plan on losing Joe (though you should still explain the situation to Joe and let him decide whether to resume relations with you after the study period). In other words, don't risk defying any of Dan's wishes unless you are okay with the possibility of losing Dan.
You could tell Dan, "I'll do as you ask this time. But I hope you're not planning to make a habit of this kind of thing."
On the other hand, everyone else that's posted here so far has a point too.