Well, although this problem is quite weird and I do not expect that anyone could help me with it, I'm posting it here for the small chance that someone could help me with it.
A couple of days ago a friend of mine brought his laptop to me with the plans of playing some games in LAN with me and my brother.
My computer is running Windows XP, my brother's computer is also running XP and my friend's laptop is running Vista.
First we downloaded Understorm's UDP Patches. Then we set up a LAN with Hamachi and all games, including RA1, worked well, with the exception of TS. We also tried playing TS via XWIS, however it didn't help at all.
Every time we started a game, we could play it for a few seconds and then we got a reconnection error. One time we could play it for a few minutes before getting an error, however it lasted that long only once.

After trying TS, we decided to play some other games, and while my friend was installing them I tried to play TS with only the two XP computers, and it worked just like it should. After doing some more testing it seems that we can play TS as long as my friend's laptop isn't participating in the game. Every time it is, we get a reconnection error in first few seconds of the game.
Btw, this wasn't the first time we tried to play TS in LAN. We tried the first time somewhere in May, when we could play TS about 30 minutes before an error occured. However 30 minutes wasn't enough even for small games, but it worked much better than it did the last time.
The next time my friend comes here with his laptop has been scheduled to next week, when I'm going to do some more testing about this. Since it was much more playable a few months ago, the first thing I'm going to do is ending all unnecessary background processes, especially the programs that he has installed in a few months, although I'm not going to start ending them aggressively because I got no idea which of those processes are Vista's system processes.
Does anyone here know what I must do to get TS working correctly?
(if it's possible to get it working correctly.. with all this testing for waveclass errors, recon. errors etc I've almost fixed it's errors as much as I've played it..)