Asking for reversing my decision after declining a PhD offer
I suggest you contact the department, minimizing overly personal details - but basically outlining that the life situation that caused you to decline their offer changed unexpectedly, and you would like to know if it would be possible to attend after all.

It is basically down to: 1) no, spot is no longer available or they can't extend/re-extend the offer, but you can probably reapply next year, no guarantees; 2) sure, that is possible, 3) it depends, they will ask additional questions or want to talk to you more before rendering a decision.

If you are professional in the communication then it will not cause everyone to look down on you, all reasonable people know life situations can change unexpectedly. It really isn't that big of a deal, they can either help or they can't/won't. 

As for who to contact, I would tend to suggest whoever contacted you with the offer and/or the person who you contacted to decline. As for what to emphasize, I'd just keep it simple and relate it most directly to why you declined in the first place, but try not to over-explain. Perhaps you just realized that there are ways to mitigate being away from family that you had not considered, or that you will have other family you can visit, or just that you'll end up having to be away from some parts of your family regardless so you'd rather persue something you are passionate about rather than stick with the familiar - etc. A sentence or two is probably all you need to include in the first contact - the situation has changed and you just want to see if attending would still be an option.

The only other thing you should be clear about is that you are in a position to accept such an offer from A - i.e., you have not already accepted a mutually-exclusive offer from another US graduate school, as that will tend to create additional bureaucratic resistance (such as needing a statement from the other school, etc.). 

It might be an option, or it just might not, but so long as you act reasonably (maybe have an especially rational friend read your email before you send it to make sure you keep it short and professional) there is no long time harm in asking. Life happens - good luck, regardless!