I just took my 11 month old. We were staying in Phoenix and made the drive over.
* The drive itself wasn't bad. You know your kid best. It took a lot of effort and energy to keep our girl entertained for the drive. (It was only 6 hours for us). That was definitely a challenge.
* The parks weren't bad at all. We did lots with her. She did: Alice in Wonderland, Peter Pan's Flight, Mr. Toad's Wild Ride, Snow White, Pinocchio, Dumbo, Haunted Mansion, Pirates of the Caribbean, Small World, It's Tough to Be A Bug, and Monsters Inc. She loved everything and actually fell asleep on Pirates. She was mad after It's Tough To Be A Bug because she wanted more.

The difficulty was in the queue. Again - sitting waiting doesn't work for a baby. But once we actually GOT to the ride, she had a fabulous time. We worked our touring such that the ONLY things we waited for were Alice in Wonderland and It's Tough To Be A Bug. We were in line for early entry at 6:30 and did the bulk of our rides during the first hour they were open. We wanted to do Nemo - but it really is a choice. Do you want to do ALL of Fantasyland, or just the Nemo subs? And I was a bit nervous about the flume drops on Pirates of the Caribbean - but she fell asleep. The boat rides (Pirates and Small World) put her to sleep. She clenched her butt cheeks up on the drops, but like I said - sleeping the whole time.
*For the other rides that she couldn't go on - we made effective use of child swap. We had a friend come with us, so nobody had to ride alone. Plus our friend got the bonus of riding twice with no wait.

And I'd HIGHLY reccomend using the child swap for a few
Disneyland exclusives. The Matterhorn and Indiana Jones come immediately to mind. I'd also reccomend doing Space Mountain. While different, it blows the Magic Kingdom's Space Mountain away!!! And while I'm thinking about this, rather than child swap, you can just use single rider lines at some of the big ones.
*I don't know if you breast or bottle feed - but there's TONS of spots to do both. There's lots of little out of the way places for some privacy if you breastfeed. Likewise, there's shaded spots where you can bottle feed out in the open. (I don't know your comfort level with breast feeding - or if you do it - so no judgements - I'm just letting you know my observations as to where you can do both!

)
*The KIDS are in charge. We had one meltdown - and it happened AS we were leaving the park. The moment those babies start to get uncontrollably tired, make your way toward the exit.
*Strollers - NOTHING like at Walt Disney World. With only a couple of exceptions, I didn't see ANY designated stroller parking. You just kind of left it. It was a bit nerve wracking at first, but we put our valuables into the diaper bag, left the stroller and it was still there when we got out.
*With 2 babies - it's gonna be tough to get family pictures so be sure and use Photopass!!!
*Even with a car, and a Good Neighbor hotel room within walking distance? You'll probably want to use the Anaheim Resort Transit. It saved a lot of walking at the end of the day.
I personally wouldn't hesitate going again with a 15 month old. But BOTH a 15 month old and a 2 month old? It'll be a challenge. But if you do decide to take it on, it will be well worth it.
If you want to check out some pictures:
http://www.theverythoughtofyou.net