Handling two (or more) groups of PCs at the same time is a very tricky area to explore. Through trial and error, I have had successes and failures, and this experience I will try to impart.
For the sake of arguing, let's take the individual reasons why the group is split up out of the equation for now, and deal with the fact that you indeed have multiple groups of PC's within the same gaming session.
go) Split-Players: I have tried splitting up the players into different rooms, but I feel like I am neglecting the side that I'm not currently giving my attention. If you do decide to split them up and take turns DMing each group, you will need to be fast on your feet. I mean this figuratively and literally. You will want to spend brief moments with each group, forcing you to hustle back and forth between the two. You will also want to be quick, clear and concise with your DMing, so that the players register all they need to know in the shortest amount of time, and are able to respond in a like manner. Spend five minutes with group go, filling them in on the situation and possibilities. Tell them you will return in five minutes for their actions or responses. Hustle over to group 2 (like Mrs. Doubtfire) and do the same. This hit-and-run technique works best with players who are as fast as the DM, and the bogs begin when the players lag behind. Generally, I run this option on rare instances (see below).
2) Combined-Players: The players in this option never leave the table, regardless of how many split parties there are. Keeping the players together allows everyone to enjoy all aspects of the game. It relies on the fact that split groups will know about most of the other group's experiences, but must restrain using out of character knowledge of those events. This is what I want! Have you ever gone to a horror flick, and saw the murderer stalking the woman in the shower? Very exciting to watch, especially when you want to yell out warnings to her, despite the fact she can't hear you. In D&D, it's great fun to watch the other group get assaulted by thugs while you're sitting in the tavern, waiting for the 'soloing players' to get with it and join with the rest of the group. Not only are you not running all about like a beheaded chicken, but the players never really experience any downtime. The game pauses briefly for one group (5 minutes is nothing, especially when you get to enjoy the activities of the other group/s), but the sense of an extended delay of game is avoided.
The only exception to this is when there is sensitive information I want to keep away from the other groups. If group go is talking to an NPC regarding a puzzle or quest, and the players of the other group are at the same table, it's impossible for them to suppress knowledge of the solution. They can say their characters don't know the answers earned by the first group, but the players themselves won't be able to role-play the wrong answers effectively. In addition, I want each player to solve puzzles and the like on their own, without being robbed by the other group's success. That's a huge chunk of the fun!
3) No-Party-Splitting: If you want to discourage the groups from splitting up, teach them that the D&D world is a dangerous place to be in when their numbers are divided. Players who get whacked upon repeatedly after going on solo missions (despite the pleas of the other players stay together) will realize that it's safer (and healthier) to stay with the larger numbers. (Ever seen Aliens? What happened when the Marines split up? Ripley needed more Marines..."Game over, man. Game OVER!")
4) Notes: Finally, the examples above generally work when split groups are allies. If you are ever in a situation where two or more groups are divided amongst themselves, you are forced into option one. Things like tactics, intentions, motivations, etc. need to be kept privy amongst that group, and discussing such things while at the table will defeat the purpose. Also, when one character is plotting something he doesn't wish the others to know about (nabbing the best gems for himself, keeping certain information from others, planning a suprise attack, etc.), it's quicker and easier to slip notes than to split off into another room.
With a bit of experimentation, you will discover the best technique for your group. If a private matter can be summarized in a sentence or two, your best bet is to use notes. Extended dialogue should be handled in brief, private discussion of no more than five minutes. Remember to keep the action moving along at a brisk pace, else the other players will become restless and the mood will be lost. You won't have to fear divided parties as long as you have a prepared plan of action on how to handle such situiations, and eventually, you just might look forward to those multiple party sessions!
