Is there a mod that exists that allows toddlers to attend preschool? If not, can someone make one? I want one that would just teach the basics (walk, talk, potty train). Maybe it could work like regular school or a job. Having the drop down and choose what you want to learn first and then just have a progression bar in the career tab with what days and times they attend.

With the Generations EP your sims can manage a nursery in their home. Teaching the tots' skills gives your sim a better work performance. Unfortunately, these are random NPC babies and parents instead of your own.

I haven't heard of one (sorry!) but as an alternative you could invite a babysitter in if you were going out. Then, using either Aurora Skies Gold Edition or buying the two items directly, you could place the toddler in the walker/playpen and they would be able to teach themselves how to walk/talk themselves and maybe pick up some logic skill too.

To make the playpen more/less mood altering (ie., use 'more' to keep your toddler happy all day while you're busy) you could use this mod: http://modthesims.info/download.php?t=497910

is there a certain walker/playpen that I have to get or do they all work the same way to teach them how to walk, talk, and potty train?

They don't teach potty training. The walker teaches walking and the playpen teaches talking, followed by charisma (if talking is completed) and possibly logic but maybe mechanical. I'm not exactly sure what the abacus skill is.

The ones I mean are found here: http://store.thesims3.com/auroraskies.html under the Gold Edition set. Whether you get them from the store or elsewhere is your own prerogative.

I'm not sure whether custom mod ones would require the above to be downloaded; you'd have to check individual specifications.