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The first thing to do would be to each of you take a towel or small blanket and let the respective dogs sleep on the towel or blanket. After a week or so, switch the towels or blankets. Wait another week so each dog is used to the other dog's scent and each one will now smell a little like the other dog.
The you will want to introduce them on neutral territory like a dog park or other enclosed area. When dogs are on their own property, they tend to be territorial an protective which can lead to aggression. Introducing them on territory that doesn't belong to either dog allows them to greet one another without worrying that one dog is in their space. Additionally, you have to try very hard to not worry about what your big boy is going to do to your sister's girl. When you worry, your dog picks up on that and then he feels that if you are worried then he has reason to be worried to and can be aggressive as a defense. So you need to relax. If your dog is comfortable at a dog park with other dogs, go there and introduce them with others around to take the pressure of a one on one meeting away.
If that isn't possible, perhaps an enclosed area like a tennis court. Leave the leashes on the dog, but they my have less issues if they just drag the leashes. If one is more dominant (probably yours) the girl can still run off and if they do end up in an altercation, you can both grab the leashes to help separate the. Usually a male will be dominant and may pin the female on the ground and cause the female to submit. This would not be that unusual. You just have to be sure they are not drawing blood.
You might also try walking the dogs together. The humans can stay between the dogs but this will also get them used to being around each other. The more time they spend close to each other, the better your chances are of hem becoming adjusted to one another. They are both mature, so I wouldn't expect a lot of playing initially, though hey might surprise me. Just take it slow.
I hope my information is helpful to you. If you need further information please feel free to reply.
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Since there have been recalls on certain foods, please check the following site to be sure the food your animals eat is not affected. If it is affected, contact your vet as soon as possible. Have your dog seen if they have any symptoms.