I don't know how to define this relationship, I have seen lot of people think that she is in love with Jack, but I don't agree, I think she is in love with his pearly white teeth, that sparkle like the snow, because I personally think that Tooth does not have time for trivial stuff like love, she doesn't have time.
I agree that she is clumsy around Jack, but mostly, because I think, before she gets to really know someone, she is like that, and the fact is, she is not like she was in the book, it's said that she hasn't gone on the field after the battle with Pitch in the past; while she acts normal around Sandy, North and Bunny, she has had contacts only with her fairies, I think she actually forgot how to act and socialize, and that makes her clumsy.
I don't and won't deny that she cares greatly about Jack, and so does he in
return, but I mostly see it as friends, I hug my male friends when I'm happy
for them or to congratulate them. In the end Jack helped her a lot too, with
the children, and with the socialization.