Competition?

So before my daughter was born, my MIL always thought that my parents would take over. I'm super super close to my mom and plus she's my mom, not you. But not once did I think she would "take over" fast forward 8 months all my MIL does is act like it's a competition. I went over to my moms for Halloween and she came over and went to get my daughter before my mom and the first thing she said was I GOT HER FIRST I GOT HER FIRST. And just other random shit these last few months like if my mom watched her for a day, my MIL would have to make sure she saw her that week. Or my mom would buy her an outfit, then so would my MIL. You catch the drift? My SO has even called her out on it and she always plays the pity card and has no idea what he's talking about. IT MAKES ME CRAZY. Is it just my family, or did you feel some competition between the Grands? (Side note, my mom feels no competition and doesn't even understand why my MIL makes deals like this. She thinks it's ridiculous)