There are 3 phases in an electricity supply system, in most cases a house is only supplied by a single phase so no problems as these devices can only connect to each other if they are on the same phase.
For more in depth info go to:
3 Phase Electricity - The 3 Phase Power Resource Site
As regards Powerline, this doesn't map 1:1 onto phases. Different types of distribution board can interrupt the signal, as can a bunch of other things.
However, there are subtly different flavours of Powerline, and whilst one flavour might not work, another might. My Netgear XE104s have been working non-stop with no issue for 5-6 years
(as well they should, seeing as i'm a Netgear Powershift Partner
)
Anyway, I would recommend Powerline over wireless bridging for this application. Also I would recommend NOT re-using another combined router/AP at the other end, as the inclusion of another set of NAT into the equation is liable to cause more headaches than remove them. Just either get a pair of these and a standalone AP like a Netgear WG102 (my preference), or get a set of WGXB102s and you should be sorted
Incidentally, before you try all this, are you sure your existing wireless is not just competing for channel bandwidth with a bunch of other APs in the vicinity? i.e. can you see other wireless networks when you do a search? Setting your AP to a non-blocking channel would also help (there's only 4 wireless channels which don't interfere with each other, despite there being 13 to choose from).
HTH. PM me if you need any more help.
Mike.