So no one would have a problem with their child's teacher running against them even though the teacher had never been involved with PTO. Plus the teacher hasn't talked to the parent about the situation before or after the election.

Tell the parent you appreciate her feelings but the PTO has moved in the direction they have in accordance with the bylaws. Give her some options on significant ways she can support the group and allow things to move forward without any more fanfare or chit chat. The more of that the more the spatter left by the injury. Really--2 good folks, 1 won....it's done.
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If she was voted in and it was done in accordance with your bylaws there isn't really much you can do, imo.

We have just had elections, and we had a teacher to run against her own room mother for an executive officer position. To top things off, no one knew in advance. The only people that knew were the nominating committee, which were all school staff members. I would appreciate some feedback on this. It has upset the mother, and the current board. We really don't know what to do.