That's okay! I don't think you sound controlling rather than just assertive and good at taking the initiative, which is always important to progress a roleplay!
As for how they meet Tsuna and the others, I guess any number of ways would work! If they share any classes/clubs (which they might decide to try attending with the hope that say, the cooking club sounds pretty benign and unlikely to be crazy like everything else), they could meet one of the members through that? Though it's a pretty big school, huh?
Considering Reborn's decided role in this little plot, I'm sure he'd make an effort to orchestrate some kind of meeting between them and the Vongola. It seems most likely that he'd send Tsuna to them first and play it off as some kind of coincidence that they met. Maybe they happen to share a common class and Reborn pulled some more strings (...or was suddenly the teacher of said class) and forced them together in a group for the day? Tsuna is the most likely to act unnerved/scared by the insanity in the school too, so maybe the girls will think they've found a kindled spirit in him at first, haha!
Aw, I like your OC!