You should get yourself a non immigrant O visa on the basis of having a Thai child. It'll give you 90 days and then you can extend for a year if you have the funds. If not a year then a 60 days extension at your local immigration office. If you're name is on the birth certificate it should be fairly straightforward. Best place to do it is Savannakhet Laos. Catch a flight to Nakhon Phanom from Don Muang. Then a mini van to the Mukdahan boarder crossing. The way the flights work out usually means you have to stay over two nights. This is your best option for now because your rights as a parent are more than just a tourist. Oh and you can also get your work permit on the visa if you manage to extend it to a year. It should be possible with either 400,000 baht deposit into your acc from abroad or a 40,000 baht income from abroad. Having this should help reduce the headache of getting a work visa and make the process of getting a work permit a bit easier.
I've heard some companies won't want to use their time and resources to do work permits at times. Tread carefully and see if you can get them to take some action.