@Michael *******
Even if you had gotten the tourist visa, you would have been denied entry again by land and air. So please do not try to get in via Nong Khai, you will 100% get denied (even without the denial entry, you would be denied).
You have a denied entry in your passport, which will be more costly to get back in. Please contact a reputable agent like
@THAI *****************************
and they can get you in. It's usually 4k baht to get in VIP/Safe entry, but because of your denied entry, it's gonna be double or triple that.
Once in Thailand, you will need to start the Non O process immediately based on Thai Child.