Is the laptop wireless enabled or did you use either a USB adapter or Wireless card? I can`t see that you should have a problem because what you have described is exactly what wireless connections should do. Which laptop have you got?
To remove the home connection you need to open the laptops wireless connection user interface and delete the home connection from the "profile" - that will stop it trying to connect. However I am sure it`s something simple to resolve - just post back and we`ll try!