Can I have POA for my mom, and not my dad?

Yes, each person designates who he or she wants to have Power Of Attorney, and if your parents choose two different people, that is their right. Of course, it's generally easier if one person handles everything, particularly with joint assets, so it could become problematic. Much would depend on the will, I'd think. If you want legal counsel, that won't hurt, either. An elder law attorney could help you sort it out.
Take care,
Carol