Girl...I know how hard it is to be a new mom with people interferring - but you're in HER house so if you really want to solve this problem - MOVE OUT.
I know she's handy to have around for babysitting and all... but MIL's are just not meant to be roomates.
I personally would do whatever I could to be on my own and all that would stop. (and if it didn't - you can always just limit the visits) It's not a competition - you are the baby's mom so I wouldn't worry about what she says. She is the GRANDMOTHER ....and if she starts acting like 'the mom' again - just say EXCUSE my baby's grandmother - she tends to be a little Possessive - maybe one day she'll get the hint
I would try to work on moving out before this becomes a huge problem in your relationship