Hi N.!
Welcome to Atlanta! I understand what you're going through completely. My kids are a little older at 5 and 7 so they are in elementary school now but they've been home for two weeks for break and I was actually grateful that school started back today!!
I agree completely with the post about MOMS Club. I just filled out my renewal this morning to send out (my 4th year of being involved in the Suwanee-East chapter). It was exactly what I was looking for. Especially if you're brand new to the area-- You automatically have 40-50 friends (depending on the size of the chapter) and lots of things are planned on the calendar-- most of them being free. The kids play while you get to make friends and have adult conversation. You can get great advice about preschools as well when you need it because some or most have already done the research and they're glad to share the information. You can get on momsclub.org if you want to check out the group as a whole or you can email ____@____.com to get in touch with the Membership VP for that chapter. You pick and choose what you want to do and playgroups are wonderful for your sanity!!! Even though my kids are in school all day I still want to be a member-- they have book club and meet for breakfast or lunch or coffee and moms night out that I still like to take part in. There is something for everybody!
I know you had mentioned finances being tight but you might want to check out pricing for just your 4 year old at preschool. It won't be the state aided Georgia pre-K program but depending on how many days she goes it can be reasonable for a few mornings a week to have the girls split up for a few hours and them they look forward to seeing each other in the afternoon. Again, the ladies in the MOMS Club chapter can give you some information if that is an option for your family.
Good luck with what you decide to do! R.