Let me see if I can communicate my thoughts on this; forgive me any inadequacies. In boxing over the years, I've noticed that WoW will do this to you under certain conditions. It seems as though certain setups (various router hardware, etc.) will suffer from longer "oops lost connection...reset" timeouts than others. Some also do not play very well with multiple clients running a bunch of streams to the same client PC (I fought that when 10-boxing with a cheapo Netgear). I presume you haven't monkeyed with your TTL or other values and aren't using some sort of "Super New And Improved Sexier Than Ever Bandwidth Speedup Connection Ping Booster Pro XL Elite" type of service? If you can eliminate all of that, you're down to eliminating your internal systems as a culprit. Now, in defense of the script-readers at Blizzard Support Bangladesh, there are cases where you can end up with problems like this only with WoW/blizzard games but not with other internet services. What would be interesting to see is if Diablo 3 kicked you off all the time, too, which would mean Blizzard's infrastructure doesn't like your setup. Then, see if you can run some other app that requires a constant connection (like some kind of streaming video or something that doesn't buffer) so you can see what's going on.

A few things you can try to help eliminate low-hanging fruit:

* Power off your dsl/cable/fiber router for a couple minutes and see if it clears up.
* Try a different router/hub.
* If you're connecting over wireless, try connecting wired or vice versa (use a different network adapter, basically)
* Open up the management page for your internet router.
** Go to the status page and see what the internet connection shows for Default Gateway. That's the IP for the router one step upstream from your modem.
** Open up a terminal/command prompt and type "ping -t 192.168.1.1" (use your Default Gateway IP instead of 192.168.1.1)
** Watch that window around the time you have connection issues. If you don't see any timeouts, that's good. After a few hours, press CTRL+C and see if it shows any packet loss. If not, that means your connection to your ISP's local hub seems to be good, which saves you a lot of headache. If you see packet loss there, you have a crappy connection to your provider and should bitch at them with lusty abandon until they fix it.
* Try playing from a friend's/family member's house at the same time your daughter is playing from home or vice versa and see if the alternate location still has a problem. If it doesn't, the problem is definitely in your house connection or that area's local provider.

Failing all that, I'm not sure what to try next. Hopefully you can try the above without too much inconvenience. Good luck!