My DS Lite won't connect with my router too, due to incompatible security system with my router. I was thinking that your situation might be the same as mine, but since you said that your 3DS XL won't connect with your local Wi-Fi either, then I dunno. :(
I'll be the first one to get that River Vivillon! While I do not collect them intentionally like the others out there, I have a box dedicated to them and so far I have only three plus one counting my own. {XD}
Are you gonna get your XY copies by Christmas? :O