[MovedGoalPosts]

The theoretical transmission range and actual transmission ranges you can get with basic wireless kit can be vastly different. If your Belkin wireless router has a good line of sight (direct) to your neigbour's house, then any other wireless access point you try to add may well not communicate adequately. If the line of sight is poor, try relocating your router first, and see if there is an adequate signal opposite before buying anything else.

What it the minimum distance between your houses? Thick walls, even glass or other things in the way could degrade a signal enough that it isn't reliable or works too slowly.

Please remember that very few ISPs will be happy if your wireless networking is being set up so that two different households can share one connection.