No point in even revisiting the first incident. Everyone agrees, including the OP, that as soon as she realized there was another totally unexpected dog on the premises hers needed to go home.
In the second case, there was absolutely NO reason her dog should have been locked in its own house. That was a yard her dog was accustomed to being in and she was in perfect health. The OP's dog did not behave badly by chasing or growling and snarling at the other dog. Apparently it didn't even bark at the visitor.
As far as Aunt and Uncle's dog being "old", if it was healthy enough to make the trip it was healthy enough to be around other healthy dogs.
Clearly the dogs themselves figured it out with no problems! Sounds like they had more sense than some of the humans here.
This really isn't much different from dealing with kids. Same rules apply.
If your child is ill with a contagious disease, then of course you do not allow your child to be around other children. But if your child is healthy and is playing in what s/he perceives to be his/her own yard, should the parents of a stranger child who happens to be visiting next door be allowed to tell you that you must keep your own non-threatening, appropriately behaving child inside? I don't think so.
Since the two yards are connected and not fenced, what if the stranger child wants to play in "your" yard? He/she isn't YOUR guest. Should you have to make your own child come inside and stare sadly out the window while the stranger plays with your swing set and sandbox?
If the kids start fighting or stealing each others toys, then you deal with that. But you don't apply artificial boundaries to the child who lives there without very good reason to do so. And you know what? Just like these dogs, most children find a way to play together peacefully.