Yamato will confront Kaidou, but i doubt they would fight seriously, but it will be a similar case to Luffy vs Garp. Kaidou certainly does have some "weird" love for Yamato, the same could be said about Yamato (she cried like mad when she found out the cuff would actually kill her).
But that confrontation won't happen anytime soon. Remember, Yamato's top priority now is to protect Momo, which she can't do if she's going to the rooftop now. That confrontation will only happen once the Alliance have dealt with the Calamities and the F6 (as well as the Big Mom pirates if they ever get there).