Firstly I hope that your own dog has a peaceful and pain-free few months. Knowing you are going to lose a much loved pet is never easy to handle as I know from past experience.
I used to foster dogs until a permanent home could be found for them and quite often ending up keeping the older/poorly ones so that they could spend their last few months in a family home as opposed to a lonely kennel.
I found that when introducing new dogs into the household ground rules had to be laid down for all concerned, both the family and the dogs.
The new dog was not to be fussed/cuddled etc for the first few days any more than the resident dog, which is hard I know, especially if it has had a rough time beforehand. Until you are certain that both dogs get on well enough, they must never be left on their own, not even for a moment. I found when first introducing the dogs that placing the new dog in a crate was the best/safest policy, that way the resident dog could sniff/suss out the newcomer but should there be any sign of aggression then both dogs would be safe as they couldn’t get to each other. If there is no hassle between the two then gradually introduce the two in the same room but keep them both on a lead/leash for the first few days. Don’t let the chance of jealousy raise it’s ugly head, if you stroke one dog then stroke the other, treats should be given at the same time, feeding bowls should be at opposite ends of the room for a while and make sure all toys are taken away so that they don’t fight over them – they can be gradually re-introduced at a later stage. Lots of walks together can also help to alleviate any built up tension. Most of all let them know that YOU are the pack leader at all times.
I hope this is of some help to you and yours and I wish you all a happy and peaceful Christmas.

Sorry, Jim

If possible have your uncle keep the dog; this time is not good to be putting that added stress on your girl. Of course you said you would separate the two when you are not home to supervise. Wise choice. Also make sure to give the two PLENTY of time away from each other. If its between putting the new female away for a little more time and making her wait, vs her going to a shelter, etc. Its worth it. She will have your home to herself in the near future.

As for the initial introduction, always start on neutral territory. When you introduce the dogs, let them say hi, then go for a walk together. That way they are around each other, but not in each others faces. take it slow. Allow your old dog to go into your home, drink, etc. Don’t let the new dog off leash right away. Take it SLOW.