I'm a PM and I can't say that it's the kind of job that has a lot of options for part-time work. Projects are more often than not very time poor and you're ultimately responsible for everything so in my experience you're never really off the clock, which has not really been conducive to any real family life.

BAs though usually juggle more than one project (if it's not too big) and could be done part time. Or a BSA job if you have specific technical skills.