If you wanted to go from 2 to 1 domain you'd have to use the ADMT to migrate the acocunt in the child domain into the parent first and then do as Celestil says with domain renaming - this is a risky process though and breaks things like Exchange.
If you are retinaing your root-child domain structure then to upgrade the domains to Windows 2003 you first have to chose between in-place upgrades or rebuilds of your DCs.
I'm going through this process myself and have chosen to do rebuilds as I want a clent build and there's some security improvements over in-place upgrades. If you chose in-place upgrades then it's a very simple process - just upgrade each DC in turn, you first have to forestprep and domainprep to support Windows 2003 AD though.
If you're doing rebuilds then it's a lot more complicated. Personally I'm starting off with the simplest DC's, i.e. the ones that don't have FSMO roles etc. If you only have two DC's currently with stuff spread between them I'd first start with a new DC (can just be a desktop PC if you only have it as a temporary solution), build that as Windows 2003 then DCPROMO it. Make it a GC and transfer everything but the PDCe and infrastructure master role to it.
Then you have to see what services the other DCs are offering besides authentication, in my case even our simplest DC is doing WINS, DHCP, DNS and TS licensing so it's a pain heh.
For DNS and WINS I just made the new 2003 DC a DNS/WINS server, the DNS is AD-integrated and I've made sure the WINS replication partners are correct.
For DHCP so far I've just changed the scopes so the point to the new server as primary DNS/WINS and left it run a few days to make sure clients are working OK.
Next I'm going to migrate the DCHP scopes following this article:
I should be able to do this during the day without disrupting clients.
After that I'm going to set up the new server as a TS licence server and authorise it, we only have 3 TS servers 2 of which already are hardcoded to point to a licence server so I'll jsut change all 3 to point to the new server.
Then I'm going to get NTP time synching working on the 2003 DC and transfer the PDCe role to it.
After that it's just a case of rebuilding the existing DCs one at a time (starting with the one without the infrastructure master role) as they aren't doing anything else. In my case I'm going to keep the first 2003 DC as a production DC (it's a new decent server) so I don't have to worry about migrating everything back again but it you're using temp hardware then you need to migrate everything back to the rebuilt DCs. In my case I'll just be adjusting DHCP to reflect secondary DNS/WINS and shuffling the roles (inc GC) around again.