[attobyte]

I don't think this is really a split personality issue.
From Season 1 we know that there were originally 108 Sekireis. Since Yume intentionally merged with Musubi (reducing the number to 107), there is little doubt she had a reason to do that.
Among the possible motives I can imagine are:
1) When she was rescued Musubi's life was in danger and Yume merged to save her;
2) Older Sekirei eventually merge with younger ones as a self preservetion mechanism (how this works is beyond me though);
3) Yume, by seen all the killing Karasuba did, decided to hand over the task of opening her heart to Musubi (this one is so off);
4) Yume tried to break free from her Sekirei project position in order to feel the love she asked Minato to teach the Sekireis or
5) Something completely different which renders all my guesses absolute nonsense. In this case I apologize.

Note that all I know about Sekirei is in the first season. I don't know the manga much less have watched ep1 of season 2.