AITA for telling my little sister that since I'm married now, we aren't immediate family anymore?

My wife and I (Both 23) got married three months ago, courthouse wedding because we're both broke. I have a little sister (10F) who really looks up to me, and lately has been wanting to spend more time with me. Which is fine, she's an awesome kid, so I try to make time when I can.

Anyway my wife was in the hospital for a few days last month because her appendix decided to shit the bed, she's fine but it was scary for a bit. My sister really likes my wife as well, and had asked if she could come to visit her with me. I explained that no, they only allowed one visitor and it had to be immediate family only.

She asked why she wasnmt considered such, since they're sisters (in-law, but she doesn't call her that) I explained that once we got married, our old immediate family became our extended family, like our cousins. Our only immediate family is eachother, and any children we eventually have.

That really upset her, and she started asking if I really only saw her like a cousin now. I said no, but she is my priority now, not her or our parents. Now she's not talking to me, and our parents think I could've handled it better. I really don't think that's true, but I could be wrong.

Update: So yeah I fucked up, I see that now. I feel like shit and deserve to, because that was such a hurtful thing to say to her. Even worse is that I was stubborn enough not to apologize for her sake. She's still not speaking to me, so I wrote a note to deliver to my parents for her (I owe them an apology too).

"(Sister), I'm so sorry that I said what I said to you, I was wrong and you are right to be as angry as you are. You're still my sister and no matter what happens that won't change, and I'm sorry that I let you think otherwise. I love youbas much as I ever did, and we're still family and always will be." I don't expect her to get over it quickly, if at all, but that's my fault.