How might I pray to Mary in helping me with my relationship with my own mother–which is not a good one!?

This is a great question, and it touches on so much of what Catholics believe about Mary. I’ll throw out a few different ideas here, and hopefully one or more of them will resonate with you.
First of all, the fact that you have the desire to heal this relationship means that you’re already on your way. I’d start by telling Mary more about the struggles you and your mom have had, and explaining why you want this relationship healed. Imagine that you’re speaking to a good girlfriend about this and asking for her prayers (that is, after all, what we do when we pray to Mary – we ask for her intercession on our behalf). You may even find that the experience of articulating all of this background helps you notice things about yourself and your feelings that you didn’t see before.
If you enjoy praying the rosary, you might try connecting each of the mysteries with some aspect of your own relationship with your mom. For example, when you meditate on the Annunciation, you could pray that you and your mom will be as open to healing as Mary was open to following God’s plan. When you pray the Visitation, you could pray that you and your mom will come to support each other just as Mary and Elizabeth did.
It might feel weird at first, but you could also try thinking of your mother as someone who needs mothering herself. Maybe there are wounds or pain your own mother has that need maternal love. Catholics believe that Mary is the universal mother, so you could ask Mary to mother your own mom, offering her comfort for whatever emotional hurts she may have.
Hopefully this gives you some ideas. Truly, there’s no right or wrong way to do this. A simple “Mary, please pray for my mom and me,” at various times of day may end up being your favorite way to pray. However you go about it, I hope that you and your mom are able to find common ground and heal what divides you. You’ll be in my prayers, too.