We love Disneyland! Be sure to check out California Adventure if you have the Park Hopper pass. They have the Playhouse Disney play/show and the parade with all the Pixar characters. What works for us best is being at the gate early and doing as many rides as possible and then going back to the hotel in the afternoon when it is crowded and take a nap. This way our kids were able to stay up for the fireworks---they were more excited for the "fake" snow that falls after the fireworks.(We live in Southern California and so any snow is good snow!)
My advice would be to plan ahead. That week will be very crowded. My favorite tool of all time (and I'm not paid to endorse them or anything) is ridemax.com. You can plug in what attractions you want to see and it will calculate the best times to avoid long lines. It's really worth the modest fee they charge.
With very young children, I would plan on getting to the park when it opens. The lines are absolutely the shortest then, and you can hit a lot of them in a row. Plan to go back to the hotel for a nap or some down time at lunch.
The best website for information and to ask specific questions is laughingplace.com. Visit their forums (you might see me there) and read through the trip planning sections. It's a really great community and I've learned a lot from them.
I would suggest heading to the back of the park (you can take the train to get there) and hitting those areas first. When we were there in November the rides at the front of the park were busy right as they opened, but everything became much more calm after the first hour. After waiting for 20 min for Astro Blaster and 30 for the car ride (can't remember the name now) the rest of the rides we chose were either walk on or only a 5 min wait.
I would rent a stroller (possibly a two kiddo one) so that you don't have as much whining about all the walking...cuz you can't reason that it would be much worse if you had taken them to Disney World. LOL!
Is this trip still on given your recent announcement? ;D
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