First, let us look at the over-all sentence structure. It is saying that a certain kind of relationship (関係) is the best. Now, what kind is that?
It is one in which 「一番好きな人どうし」 can maintain a 「一番好きでいられる」 type of situation. Are you following?
「一番好きな人どうし」 means "two people who truly love each other (the best)"
「一番好きでいられる」 means "could keep loving each other the best"
Put it altogether and you will have:
"I believe that it would be the best (kind of) relationship if two people loving each other the best could maintain that relationship."
"I believe that a relationship in which two people who love each other the best could keep loving each other the best would be the best (kind of) relationship."
Wordy, I know, but that is how the original is.