My wife and I recently moved into a house with a porch swing. The roof of the house creates a private domain (reshut hayachid) for a portion of the front of the house, and this porch swing is so close to this line that it moves back and forth between domains when pushed (there’s no eruv). Is there any issur against swinging on it or pushing the swing with kids on it? (assuming the swinging kid isn’t carrying anything). We do plan to build an eruv in the front yard to avoid this problem and others. But in the meantime I am not sure what to tell my kids, so I let them swing themselves, but I don’t push them.

Technically it should be allowed,as the swing does not come to rest in the domain not under the roof. However, one is not allowed to put one's hand out a window even if his intention is to immediately pull back the hand. The cases may be different, but I suggest you put up the eruv.