Do Shia'a believe/follow Islam?

we have more than three eids . some are national and some are religouis. but the ones we call them eids of islam are ghorban , ghadir and mab`ath. we believe that Ali is khalife and his family too. so we celebrate the time our prophet choose him to rule after him. and i don`t think it is correct to say the ones who don`t have ur idea are not muslim ,how do u know ur idea is correct?