Do they go through phases of not wanting to go? I'm sure this is just separation anxiety, but DD goes to daycare one day a week and for the last few weeks, has been crying when I drop her off, saying 'Mommy' and 'Home' and not letting me put her down.

It's so sad. This is just a passing phase, right?
Re: If your DC goes to childcare...
I think it's the age. My nephew who started pre-school at 2 1/2 went through the same thing. But, he'd be fine and happy as soon as my SIL left.
My 3 year old goes to pre-school twice a week and LOVES it. I also attend a Moms group twice a month through the same church that does the pre-school and they provide childcare in rooms split by age. When I drop Paige to the 3 year old room everyone is always happy to go but when I drop Sarah to the 1-2 year old room both she and a lot of the other kids are crying. They distract them right away and in a moment or two it's all forgotten and they are having a great time.