Tm6 is your arrival/departure slip that you filled in on arrival., half went to immigration leaving you the other half to be submitted on your departure.
I know a few couples who straddle the 50year age, the older gets the non-0 (>50) and subsequent extensions and the younger gets a non-0 and extensions based on marriage to the other. This also applies to married couples both over 50, - only one needs to meet the non-0 (>50) requirements and the other can "trail" on the 'primary' visa/extension.
That you hadn't realised / thought of, or been told of this way for you and your wife is any ones guess. BUT on the good side, you know now :-)
On an aside does seem to be a little discriminatory against singles >50.
With the non-0 you're limited to 90 days after which you're gonna need to have to get an 12 month extension of stay in-country - or another visa solution. (UK do not issue a year long multi entry non-0 any more)
On the 0-A you can get up to 2 years stay in Thailand. (Without the need to move any money to Thailand)
If you can wait out the time for the financials to come good, and sort the medical cert' / other requirements in the UK then 100% go for the Non-0A.
Your non-0A is a multi entry and gives you 12 months each entry whilst its valid (in your case until Feb 2020). You do not need a reentry permit (tm8) whilst the visa is valid.
If you do an out/in just before the visa expires (Feb 2020) you'll get another 12 months, I.e. Feb 2021. IF you leave during this period you WILL need a reentry permit to keep the Feb 2021 "permitted to stay"
one month ago all was needed was financials (bank book / statement) and onward travel (air ticket) :- they did not require / ask for anything about accommodation.
A single entry tourist visa is valid for 90 days. On entering you'll get stamped in for 60 days.
As for waiting before entering Thailand there should be no reason / benefit why you don't go straight to the border and enter Thailand.
Of course if you have an extensive history of back to back SETV / visa exempt you could be "interviewed" by the immigration officer. Although very unlikely at either the Nong khai or mukdahan crossing.
So you're looking for a "visa" solution for your child.
That's now beyond my knowledge (I'm sure more knowledgeable people will chip in soon) except :- children cannot/do not get fined etc for staying/overstaying any visa entry.