Am I the bad guy in this?

You are right your Mom should teach the kids manors now or they will grow up thinking everything in life should be handed to them. But they are just kids so there always going to run around the house, make the dogs bark, hit each other, leave messes all over, etc. Also, your mom is there grandma so she is going to spoil them regardless of what you say. If your mom wants to spoil them let her she probably feels sorry that they got taken away from there mother (i know i would feel sorry).