My parents are obsessed with my baby!!!

I have a 10 week old son. Not only is he my first but he's my parents first grandchild. My husband & I live only 10 minutes from them. We actually moved to this state after getting married so we would be near them. I have (more like had) a wonderful relationship with them but ever since my son was born they drive me CRAZY!! I am a stay at home mom and absolutely love it. My son is our rainbow baby and I just adore him. We visit my parents at least once a week and usually more. They hold him, play with him etc. Yet they continue to nag me about letting them babysit without me there. They are now even offering to pay my husband and I to go out for a night and leave the baby with them. I exclusively breastfeed & have used this as an excuse many times for reasons not to leave him. They tell me to pump which I hate to do & only do it when I leave baby with husband (which I've only done like twice). They have now become rude about the whole thing. My mom gets angry and it's very clear her feelings are badly hurt. I feel bad about this because like I said, we used to be very close. But I just don't understand why the time she does get with my child isn't enough. My husband's parents live 1000 miles away and haven't even met baby yet! She should feel lucky to see him weekly! They have started saying subtle rude things to me calling me "momzilla" or saying I'm being rude, mean or selfish. My mom will take my baby from me and go into another room & say things to him like "you don't like your mommy, you want grandma! Your mommy is mean & nasty". I know he doesn't understand her but it really bugs me still. My mom was mad when I got pregnant & complained that I got pregnant too soon for my entire pregnancy. Now when we come over she hogs the baby the entire time, holds him for hours! When she gets him she smells him and says "this is my therapy each week. I need him to lower my blood pressure". I'm like okay he's a PERSON not some kind of stress ball. It creeps me out. I post pictures with baby a lot & my dad recently said that I only post pictures where I look good even if baby looks awful because I "only care about myself". I know it seems like a silly thing to be upset over but it really hurt! I love my child more than life itself. A 10 week old doesn't always pose perfectly for pictures but let me tell you my son always looks good to me lol. But to be told I only care about myself was really hurtful. I'm also very sensitive since having baby which doesn't help things. I'm to the point where I want to avoid them. But then I feel bad because I know they just want to be with my child because they love him so much. But I'm sooo fed up. Am I being unreasonable??