It's very relaxed here in regards to bringing your kids places. Maybe there's a place to learn Thai that also has a space for your kid to be when you're in lessons.
The list of potential problems and dangers of traveling by bus from Bangkok to Phnom Penh are endless. I'd highly suggest to fly and save yourself trouble.
no you can leave and do this alone. You just need to have the correct original documents with you. Sometimes you'll need a letter of invitation from the mother/wife. Thai embassy Savannakhet have list of everything you will need and the last time I checked it was all correct. They even answer the phone ha ha.