Is Umrah invalid if a woman performs it while wearing an abaya whose ritual purity is doubtful, given that it is used for daily activities that may expose it to impurity from dog saliva or feces, knowing that the mother washed the abayas but without specifying whether this particular abaya was among them or not?

The default state of things is purity, and a ruling of impurity for clothes or other items is not made based merely on doubt. If you are not certain of the abaya's impurity, then you may wear it during Umrah, and your Umrah will be valid and sufficient, because the abaya is ruled pure unless you are certain of its impurity.