<<If a personal representative (executor, administrator, etc.) has been appointed, that person signs for your father. If none has been appointed, your mother can sign as surviving spouse.>>

So far none has been appointed so my mother will sign the joint tax return for him. Excuse me if this a dumb question: does my mother sign her name or my father's name?

Usually on certain legal documents, my mother would sign HER name and next to the signature, put down "for XXXXXX (my father's name)".

.foolseb.