Ok, that explains a lot, I was under the impression that the WG and Domain
were on same physical subnet. Since that is not the case, the way you are
logging in (with local administrator account) is correct, although I would
suggest renaming it. If you were using the domain account (which can be
cached when not connected to the domain) you might have problems.
As for the reliability factor, it should not have anything to do with the WG
and Domain situation, this is a common setup for people who bring laptops
home from work. I use the same myself.
You might want to check the linkspeed/duplex settings on the nics to see if
they match (don't use autodetect). Make sure you don't have a roaming
profile. There are advanced tools like perfmon that you can use to watch
your network connections. If you can isolate the exact errors (event logs)
and find out when they occur, you can search the internet(google), not just
MS KB for possible solutions.
BTW, I'm just curious, did you name the workgroup the same as your work
domain?