Trying not to be too anxious would be good, but direct family support in the experiment to help your Mom cut down is lovely, I think. It will either be successful, or it will demonstrate to all that she has crossed over, as we say. She may be willing to quit outright if moderation is too uncomfortable. Support and honesty within your family will be a good head start for all.
Just keep eyes open, and if your Mom becomes unwilling to moderate or to stop...you and your dad will need support of others living with active addiction.