Actually, I had this problem when I was trying to use mobile hotspotting as the WiFi for my game. What the problem is boils down to something called a NAT (Network Address Translation), which is like the community streets of the Internet that are inside of your house. What I mean by that is that once it hits the modem and router, the ISP then issues different "house numbers" and "streets" (aka the last few numbers on an IP address). However, the ISP gives each of the streets a different amount of allowed traffic and paves them different. For most people, however, you are only looking at three types of NATs:
Type 1: Open - You have nothing that would interfere with the connection to/from the console (3DS, in this case) and the game (AC:NL). However, this is extremely rare, even more so with it needing wireless Internet to start with.
This is like the entry way to the community, and is pretty much only accessed through the cable proper.
Type 2: Moderate - You have some interference but it doesn't drastically limit and/or close up the port(s) that are needed to play the game online.
The secondary roads that are respectfully done up, albeit with a few bumps or minor problems, but nothing major - This is the one you want to try to get one, if you cannot get on a NAT 1.
Type 3: Strict - This is the one that causes the most problems because, as the name implies, it is strict and will severely limit which port(s) can be used. Often times, it is the ports that are needed for game play online.
The roads that seem to be forgotten by the city and are asphalt at best and nearly non-existent at worst, which makes it hard for data to travel down.
Beyond this, I wouldn't be able to help you out as I do not how to change setting in the routers, modems, and so forth to allow for a NAT Type change. Furthermore, if you are using a WiFi not directly owned by you (aka Dorm, Library, Apartment, etc), it may be impossible to change it.
