Am I being too sensitive for not letting my parents visit my newborn after they called my birth "not a big deal"?

Hi everyone. Throwaway because my family is on Reddit.

I (31F) gave birth to my first child three weeks ago. It was a traumatic delivery — emergency C-section after 26 hours of labor. I lost a lot of blood. I'm still recovering. My husband has been incredible.

My parents live in another state. They wanted to visit immediately after the birth. I asked them to wait a few weeks so I could heal. My mother said, "You're being dramatic. Women have babies every day. It's not a big deal."

I said, "I had major surgery. It is a big deal." She said, "Fine, we'll wait. But you're being too sensitive."

They arrived yesterday. The first thing my mother said when she walked in was, "Wow, you still look pregnant." Then she picked up the baby without asking, and when I said "Please wash your hands first," she rolled her eyes and said, "I'm his grandmother. I'm not going to hurt him."

Last night, the baby was crying for hours. I was exhausted. My mother came into the nursery and said, "You know, if you just let him cry it out, he'd sleep better. You're making him too dependent." I said, "He's three weeks old. You can't sleep train a newborn." She said, "See, this is why you're so sensitive. You can't take advice."

I told my husband I wanted them to leave. He said, "It's your call. They're your parents."

I told my parents this morning that they need to go. My mother burst into tears. She said I'm "cruel" and "hormonal" and that I'm "keeping their grandchild from them." My father said, "This is what happens when you have a daughter who's too sensitive."

Now my sister is texting me, saying I'm "overreacting" and that I should "just let mom help." My mother posted a vague Facebook status about "daughters who forget who raised them."

I feel like I'm drowning. My baby is healthy. I'm recovering. But I'm being told I'm cruel for asking for space. Am I being too sensitive?