subject verb and pronoun antecedent agreement

Incorrect- Either your children or your spouse have left a mess in the kitchen.

I think it should read...
Either your children or your spouse has left a mess in the kitchen.

Either is singular so I should change have to has, however my spell check is saying I should change children to child if I want to use has.

Also,

Incorrect-The play will be attended by Theresa and myself.

I think-
Theresa and I will attend the play.

Am I correct or should I listen to my computer?

Thanks
Sherri