Third Quarter Prep for Squatober

I'm not a new lifter by any means, but I confess I'm not big into mobility. I want to participate in squatober this year, but I'm afraid injury is quite likely given how stiff I've become, especially in the hips and spine. I'll be turning 36 in August and have two young boys who's current favorite activity is jumping off furniture on to daddy. It's fun, but I'm starting to feel that too.

I know mobility work is the answer, but I want to make sure I'm doing the right things. If you were in my shoes, how would you maximize 3rd quarter prep for Squatober? Any programming suggestions for mobility or specific strengthening of stabilizer muscles?