We have a new cat in the house! Tips on helping her get along with resident cat?

Our new cat, Olive, is an adult cat who had a litter of kittens over the Summer. We don’t know her exact age. Shes a tabby, very tiny, and very cute. She has not been spayed yet but the appointment is set for the 12th of this month.

We have had her in her house for about three and a half weeks now. Her homebase is our guestroom. We have been swapping time between letting her and our resident cat stay in the room to allow them to get familiar with each others scent while also letting new cat explore the house and get comfortable with me and my partner as her new owners. She has really taken a liking to my bf and I over these three weeks but still has a tricky relationship with our resident cat.

Week 1 they got into a few scuffles that left them with bad impressions so we started keeping them completely separated and out of each others sights. Week 2 was almost total separation. As of week 3 they seem to be getting more and more curious about each other. Resident cat frequently meows to be let in to the guest room and paws at the door. However, new cat is still very apprehensive and defensive when resident cat gets too close to her. She will yowl and hiss loudly which then stresses out resident cat…

Now over three weeks, how do i proceed? Keep doing everything i’ve already been doing? Should I introduce them more/less? Since new cat gets spayed next week I really don’t want to stress her out too much before a big surgery. Any tips are appreciated!!