I think you've discovered one of the great keys to living well. When you have something constructive to put your attention and energies into . .
something you've chosen as a project to advance your own goals . . . then something in your life that's distressing, like the impact of your mother's behavior, gets crowded out. That's the best thing that can happen.

Someone like your mother is looking to take up a lot of space in your mind. By acting distant, she's actually looking to get under your skin. She enjoys unsettling you. It's a kind of power. Her plan gets foiled when you are, basically, too busy to care. Good luck with the move.