Dec 2001 was my first trip with a baby and there for, first with baby swap.
We found it interesting that some rides gave you a "fast pass" for the second parent, and others lead you around back to trade off with the baby. Trading off is much faster, the fast pass takes about 10 mintues longer. I asked a cast memeber how the baby swap ticket were any different then a fast pass, he said that more then one person (up to 3 I belive) can use one ticket. Your older child can ride the ride 2 times.
Here is how it worked for us.
MK:
SM and TM, BS ticket (didn't do SP didn't feel like getting wet) Skiped AI all together.
AK, Dino: lead you around back
Epcot: Test Track : around back
MGM RR, around back. Start Tours, one parent went on the ride,(mom) the other (dad) stood in line with the kid, when the first ride was over dad walked on with baby, passed her on to mom who walked out and dad rode. Didn't feel like TT this trip.
Most other rides the baby went with us and liked it, even the safri at AK. (oh yah, she didn't like the 3 4 movies.)
I think with this method you can use one fast pass to get both parents in. When we were there, it wasn't that busy and didn't really need them.
With the BS tickets one parent can go on a different ride, while the first parent rides and trade off.
Have a great trip.