It's a stupid request...birth certificates can take months to request from authorities in certain countries if you can even request one at all. It sounds like these embassies are doing this as a roundabout way of denying people.
Nope. My wife wasn't asked for this. What would it prove anyway? She's not 5 years old. A passport and national ID card are what is needed not a useless birth certificate.
Not suspicious. People in good health can train in Muay Thai even if they're older. That stated, remember, it's Thailand, where some people believe that once you hit 50, you're too old to drive and where I've seen 60 year Olds who look like they're 85 and can barely walk.
Even easier is to get everyone in a van for the comfortable 4 hour drive to Ranong. An easy day trip, or better yet, excuse to see some islands off the coast of Southern Myanmar for a few days (it's very safe there).
Almost certainly, if funds are demanded on entry it will be the 20K in cash not 500K in the bank. Immigration won't accept any funds in electronic form at the borders. It's strictly cash only.
A DTV isn't a viable long term residency option. In the meantime, you can easily pack the kids into a minivan and drive to Ranong, pay an agent and do an in/out to activate a new stay. I'd recommend staying the night in Myanmar, perhaps checking out the islands. Should be very doable once every 6 or 12 months and in the longer term, there's no guarantee re-entry on a DTV will always be straightforward.