Good job rescuing this 3 year old! She is going to show you love many times over.
I keep them separate for 1 to 3 weeks. I have towels in their bedding, then start switching the towels so both can get the scent of the other one. Initially I only let them out together when I home AND HAVE THE TIME to observe them. Keep a water squirt bottle handy, to break up any interactions that get out of hand. Expect some hissing perhaps even a growl once or twice. NO charging one another allowed! (I don't know if the older one will bother with charging, doesn't sound like it.)
It doesn't sound like you will have much trouble, the young one is used to living with others, and the older one likely just wants to be left alone (From the other cat, not from you, lol). So expect that they will be able to live in peace, don't expect them to be best buddies and play together.
Be sure you have at least 2 litter boxes, not set next to each other. Sometimes in the early stages, one cat will 'guard' the boxes and not allow the other to use them. Hence, separate the boxes, and only one can be guarded at a time. You may want to feed them separately for a time as well, but eventually you can just set out one bowl and they will munch from it.
I said 1 to 3 weeks, I base this on how they are with the switched towels, and my patience dealing with the closed door, etc. You may bring them out when you are available to watch, then put them back in separate rooms while you cook, clean, even watching TV (especially if you are into the Olympics just now) your attention is not going to be wholly on them. Over time, let each take a turn being closed in the bedroom while the other has the whole house and access to you. Remember, the newbie needs time out and about to learn her way around the house, find where you keep things, the good places to jump up or crawl under in case she wants to retreat from the other one. So don't always keep her in the separate room.
If you can, you may want to keep them separate until after she recovers from her spay. Even if you have them out together, consider separating them again while she is healing, you don't want her to jump or run and open her surgery site.
Only issue I can see you may have is, the 3 year old will want to try and play with the oldie, and he may just not be up to it. If she pays attention, he will let her know to go away, stop, etc. and she will leave him be. If she is too full of young cat energy to pay attention to his warnings, he may have to snarl, swat her, etc to get her to mind her elders!
Good luck, let us know how it goes and share some photos!!!
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