What would be less stressful for my dogs?

Ultimately, only your dogs can decide what they will find most stressful, and the answer might be different for each dog. Given the safety issues (especially where there are young children involved), I would recommend keeping the dogs with you. Kids just aren't very good at leaving dogs alone when they want to be left alone, and you won't be around to supervise and enforce boundaries. It would just be a dangerous situation leaving a dog who doesn't like children and a dog who is nervous around children in a houseful of unfamiliar people without their owner. If I were in your position, I'd keep the dogs with me, and try to provide them with as much of home as you can; bring their bedding (not freshly washed), maybe a rug for the border collie, and set them up with a little safe space for when you're out where they can feel comfortable and secure.

I would keep them with you. At your bf's house, provide blankets on the hardwood for him to be on. In both places, provide each with a kennel kept open for them to have a safe place.

The best way for dogs and humans to bond fast and most efficiently is taking a walk together and given treats by the person they are most uncomfortable with. By walking together with confident and relaxation, it gives the dog a sense of peace. When the owner of the dog is nervous your dog will do the same. Keeping a relaxed mind puts the dog at ease. If I were in your position I would keep the dog with you but I would time to time take the dogs to your aunt's house. For dogs exposing new things is good and help them know more than they know. Also it helps them to have a balanced life. One tip is think about what is best for you and your dogs. Pick the way that you think will be less stressing. I hope my advice would help as much as possible even though it is a bit late. Best of luck!

Your dogs will feel comfortable wherever you are at. You are their owner and they look to you for guidance. I would definitely take them where I go. Plenty of people go on vacation with their dog, they stay at a hotel (unfamiliar surroundings) and yet they are fine because they are with their owner. I would not leave them with your family without you being there. Try to keep their environment as close to normal as possible. Their beds, blankets, toy, etc. This is just temporary so I think they will be fine being away from your regular home, but I don't think they will be fine without you.

A lot of the commentary in the other comments is great advice. My addition here is perhaps try a ThunderShirt. These can help calm your pet if the above actions don’t seem to be helping much.

I’d also suggest not bringing your pets into a full room. Try introducing people slowly, rather than all at once. That way, it’s not as overwhelming. My family chihuahua hates a crowded room.