My kitten, Gema, is about 7 months old, and although we’ve had her for a few months, we are just now introducing her to the entire house (she was sick, broke her leg, etc etc so she’s been in her kitty bedroom until this point). We have a 12 yr old cat, Winston, who chills by the bun and is friendly with him, so we’ve never had this problem before. She’s been fairly uninterested in Lenny’s (the rabbit) playpen, but she just discovered today that she can climb it and hang out in there with him. She actually broke her leg by climbing a cage like his, so we’re pretty nervous about that.
I could move bun in a spare bedroom we have, but I really like where his setup currently is. He’s very central so he can feel involved, but there’s not a way to block the room off entirely from the kitten.
So my question is: Has anyone else had an issue with an adventurous kitten?
Here’s a pic of his little xpen setup we have to see what we’re working with here (if the pic works, please ignore the mess!)

Thanks for the help!