You say that:
Mind you throughout the conversation flirtatious jabs were exchanged and she wished I was with her
This definitely influences the way that we should interpret the part that's confusing you. Let's take a look at what you said:
ME - Hope she gets better and you’ll never ever have to see me or that hospital again
You are expressing a wish, and two expected outcomes of that wish. The wish is that the girl's mother gets better. The expected outcomes are that a.) the girl won't have to see the hospital again b.) she won't have to see you again.
Now we can look at her response to that:
GIRL-Thanks. Hospital. Yeah. You. We’ll see about that :)
She is very likely expressing a wish to see you again in the future. Let's break up what she said.
First, she's thanking you for what I described as your wish above - that her mother will regain her health. Then, she's breaking up what you expressed as a single thought into two thoughts - you said "me or that hospital", lumping yourself with the hospital. She's now splitting "Hospital" on its own, separating it from you. So, that "Hospital. Yeah." is agreeing with your expected outcome of not having to see the hospital again.
Then she goes on to say "You. We'll see about that :)"
You said in your post that she said that she wished that you were with her. So what's she's saying with this is, after separating the hospital and you in your expected outcomes, she's saying that "We'll see about that :)" and disputing your expected outcome of not seeing you again. The smiley, which is a happy face, shows that she's not being pessimistic about her mother recovering, as @Shoe claims - if that were the case then a sad emoji would be appropriate.
So, all in all, everything points to her disputing your expected outcome of not seeing you after her mother is better, and is expressing a wish to see you again.