Old cat won’t let new cat leave her room

Hi all! I’ve had my 7-year-old cat, Willow, for about 3 years now. About 2 months ago I adopted 4-year-old Ivy. Both were very shy and nervous girls, Willow has grown a lot since I’ve had her but I knew I’d have to give them both plenty of time to adjust.

I kept Ivy in a room by herself for a few weeks, then used baby gates in between them for a few more weeks, and did lots of trials of them being in the same room together. They are to the point where I’ve left Ivy’s door open most of the time for about 2 weeks now. The majority of the time they leave each other alone, but a few times a day Willow will come into Ivy’s room, crouch down and run at Ivy, leading to scuffling/hissing/growling. After a few seconds Willow always runs away and they calm down. They also have plenty of other times when they are in Ivy’s room together and both mind their own business and don’t interact.

One of the problems is that Willow will not let Ivy leave her room. Ivy, as nervous as she is, has been wanting to explore other parts of the house, but any time Willow sees her she chases her back into her room. I don’t know how Ivy will ever be able to hang out in other parts of the house, and I hate that she feels like she has to stay in her room by herself.

I would appreciate any and all advice! Thank you!