My son is 18 months, and we regularly hang with other kids a little older and a little younger. One thing I've noticed is that kids that age don't really play well together - or at all. Mostly their play is a battle in who gets to hold what toy, and to the loser goes the long screams and tears of frustration, while the winner just gives you a "What? I didn't do it" expression. (This is, actually, exactly what just happened in my living room about 20 minutes ago between my son and his 23-month old "best friend", who see each other two or three times a week and are generally on extremely good terms.) Kids this age get into squabbles over stupid stuff. It's because they don't understand the concept of sharing, they only know themselves and everything is THEIRS. Your job is to be patient, try to give them both the attention they need....and have two of everything they fight over. If you can't have two of things (like that super special toy truck or doll), if they continue to squabble over it - well, the doll obviously needs to go in time out. And take away the doll from BOTH of them. Direct their attentions elsewhere. If whatever you find is entertaining enough, they're both likely to forget the doll within minutes. Good luck!