Is it permissible to fast one day and break the fast the next with the the mother's permission, while assuming she would prefer me to limit my fasting to Mondays and Thursdays?

As long as your mother has given you permission to fast every other day, there is no blame upon you, and acceptance is hoped for you. It cannot be said that your fasting is not accepted. If you break your fast seeking her known love for you to break it, then you are upon goodness and righteousness, for doing what your mother loves is part of righteousness, and seeking her pleasure is desired. For in the hadith (definition): "The Lord's pleasure is in the parent's pleasure."