Need to know perhaps a little bit more but in principle the wireless router attaches to your phone line (BT I presume) and then we connect your Tiny PC to the router, either with a wireless USB adapter or an internal ethernet card with cable. The laptop I presume is wireless enabled anyway? Obviously all needs to be configured but that can be done fairly painlessly.
Exactly which router make and model is it? Are both on XP? Does the Tiny PC already have an ethernet card. (Some of them did - so tell us which model Tiny it is)
You can do this all in stages to avoid disruption and if all goes pear shaped simply revert back to your current configuration. For example we could set up a wireless link between the router and laptop first and then try to connect that to AOL BB without touching your computer. Then if we have difficulty you can simply unplug the new router and plug your old one back in!
Once we have your daughter online with the wireless we can connect your PC. Finally we donate the old Voyager to charity and set up a network so your daughter can use the printer and swap files between both computers.
By the way, you won`t get any help from AOL with this. They will want to charge you for their Gold Service at an extra £6 per month. Let`s see where we get first.