piratecat - where T-Mobile more specific about it being a temporary problem ? What problem did they say there is, or did you get the impression that 'no/slow connection' is what they expect at your postcode ?
FWIW, I have seen situations where the Three software on this laptop suggests "no coverage" yet I am connected. Admittedly there are 3x Three masts in the area (because some 'A' road goes around a hill and down a cutting, so they seem to have more cells to ensure voice calls don't die), but I'm often making my PC connect using the Windows XP 'Network Connections' method.
The 'dongle' is made to look like some Dial-Up modem and is listed as Dial-Up. I can hightlight the entry ("1.3G" on my PC) and either press Enter (to start connection) or right-click to get 'Connect' option.
Meanwhile the "3Connect" software (which can show data traffic count, and duration of connection) says "No Network".
So first I'd say, don't give up on this, just yet - it might work even if it suggests there is no chance. Second I'd say that any signal strength info shown by software might be wrong - sometimes the Three software shows 3 bars (out of 10, 3 is the highest I have ever seen) yet connection works when it goes to 2,1 or 0 bars (!)
Finally, unless there's a strong reason for DD using the dongle, it should be possible to use the laptop with your home broadband connection, either with a cable, or using wi-fi (if you already have a wi-fi router).
OK, it won't be as 'portable' as it would if she needed to take the laptop out of your home (but is that sensible anyway - not that I don't trust DD, just worried about her being mugged for it, given businessmen are mugged, and a laptop is presumably easy to sell via a fence).
Did the dongle come with a USB extension cable ? The one had something like a 2' white USB cable, so it wouldbe easy to change the position of the dongle without moving the laptop to some unusable position.
PS Have been using Three since October 2008, initially upstairs, now down in lounge, so again would say "Don't give up"