Puppy & senior dog not getting along. Is it fixable?

I recently got a toy poodle puppy. He is 9 weeks old.

My mom has a cocker spaniel, she is 11 years old.

We introduced them slowly. They have separate spaces to eat, separate spaces for their water bowls, separate sleeping areas and during the day the pup isn’t allowed upstairs with the older dog (at the moment, he just can’t get up the stairs, but once he masters that we’ll start closing the gate over if she seems like she needs some space). We wanted to make sure the older girl has somewhere to go when she’s tired of him. We have baby gates etc. and the puppy has a crate.

Since we got the puppy, my mom’s dog has been scared of him. When he started trying to get her to play, she’d act terrified. She’s very territorial of my mom, and doesn’t like the pup being near her. She acts very agitated when he is anywhere near my mom. When he is annoying her with attempts at play, she just runs. She won’t bark or anything, so he thinks it’s a game still. We intervene at this point, because we don’t want her to be stressed out. They’re never unsupervised together.

I’m panicking. I can’t see a future where she doesn’t hate the pup, and I’m at a loss on how to make it easier on both of them. He doesn’t seem to be able to tell she isn’t playing, and she doesn’t seem willing to communicate this to the puppy. Our intervention doesn’t seem to be helping the situation, and I’m not sure how to let the puppy know the older dog doesn’t like roughhousing.

Is there anything that can be done to help them get along? Or are they just too different? Will we just always need to keep them mostly separate?

Before puppy arrived, my mom had two dogs. Her other dog passed away just before Xmas, the puppy arrived last week. Older dog had been really lonely after the death, so we thought she might like the company (and I’d been planning on getting a pup for a while).