Connecting Two Wireless Computers Without A Router

This is for my parents house. They have high-speed net that can only be registered to one computer, so running it to a router and then computers is not an option. We used to have it setup with net into "computer 1" then out to the wireless router. The new computer has only one ethernet port, so this can no longer be accomplished without buying another card, which I am very inclined to do. They are getting another computer that will also have Windows 7 and would like to get wireless working again, so...

1) I've tried an ad-hoc connection. I understand the concept and had it working for awhile but found it to be "finiky." I would always have to restart the connection everytime I wanted to use it. I couldn't get it to "stick." Did I maybe do something wrong or is there no way to keep the net connection open? I "saved" the network and set it to start automatically, but it would always close the internet sharing.

2) I haven't messed with home group...will this feature accomplish internet sharing easily??...without messing with any ad-hoc crap? I need everything as simple as possible, so if they have any problems I can fix it over the phone or they can figure everything out for themselves.

Like I said, worst comes to worst, I'll get them another ethernet and run it the old way...was just hoping I could simplify things and save some money.