How do I tell a friend I don't want her there when I'm meeting our mutual friend

Basically what the title says, I've known (mutual) for around 8+ years, she's lived in my city for 4 but we'd hardly met once or twice due to distance and monetary issues w travelling. We've become INSANELY close. I'd consider her my platonic soulmate if anything. She moved away to a different state and we've kept daily contact, around 2 yrs ago she introduced me to someone she knew when she lived her and we've all sort of become a trio. Anyway I've just recently collected enough to go meet her for a week but new friend says she suddenly wants to come with, thing is she saw her everyday for two years when she was here because of school.

I want some private time with her and I'd really prefer if she came at a different time yk? But new friend is very sensitive w this stuff and spirals if we even try to say that she and I have known each other longer or that I'm closer with her (for context she's helped me thru the time I was assaulted and me thru her parents divorce) ofc I cherish new friend but again I just want some one on one time with the other one.

Btw mutual friend says she understands me wanting to meet her alone and will support me if I tell the other no.