We've flown tons of southwest flights with our now 2.5 year old. Flying with a newborn is actually easier than with a toddler, but having twins more than doubles the degree of difficulty.

If your SO gets an A boarding pass, I would line up and board with her. Although lately checking in at T-24 has gotten us boarding passes in the A-50's so it may not matter much if you wait for family boarding.

A couple of tips we've picked up:

1. try to nurse or give a bottle on the altitude-changing parts of the flights. It will help equalize the pressure in the ears.
2. have a few plastic grocery sacks in the diaper bag to bag up stinky diapers if you can't make it to the lav for proper disposal.
3. you will have to put the stroller/car seat through the xray machine at security so don't load it up with stuff thinking that you can just roll it through.
4. make sure you gate check with the counter agent at the gate ahead of time - don't wait until the gate agent has started into the boarding announcement.

good luck!