hi V.,
First you shouldn't worry about pottytraining, there is a lot of support in daycares and people there have a lot of experience. My little girl wouldn't go... she was 32 months. I told her, if you do, you go to daycare, have fun with other kids etc. actually I had her registered and the weekend before (!!!) diapers were past ... day and night ... no accidents, just like that.
I tried to find the same you're looking for, when moved here mid-summer. There is nothing free until they turn 4 and go to public school. The best prices are in church programmes.
We started with Primrose school which is one of the best in the area and very close to you.
They accept kids 2-3 days a week if available. We couldn't afford full time and she was there 2 days. But she didn't like it since all the other kids were fultime. I also believe another reason is that she was the only bilingual.
We switced to a church programme and she loves it... and is less money too.
There is a church close to you, I don't recall the name now, but it's on Pineville-Matthews and Park Cedar.
Hope this helps, if I can help you in any way, please e-mail me.
S.