you need to talk to your new employer asap. If you have a gap between finishing this job and staring the next of more than 7 days, you are going to have issues. Work visas and extensions are totally reliant on paperwork and co operation from your employer. Note . Children under the age of 18 are not subject to overstay fines. But if you have that, getting a new visa or transfer will be a headache.
Go to migration asap and talk to an officer about your situation and do whatever they tell you, or you both may end up having to.leave the country and reapply for visas all over again. Your child relies totally on you having permission to stay.
. Technically, if you are on an extension, you have seven days to leave thailand or transfer sponsorship of visa/ext to new employer. That time starts on your last day of employment. Same rules for your child. Child's visa is dependant on your visa status.
. Changwattana is 21 days under consideration now. I thought they made a mistake on the stamp and they said it's been reduced. Collected yearly extension 3 weeks later.