I have a Lao wife too, and our son is only British. His school prefer the kids to have visas/Extensions and he's always piggy-backed on my work extension, as does my wife. I don't think it's a great idea for kids to have overstay stamps, even if they are not fined, especially if they'll be living/studying in Thailand for a long time.
Thanks. Yes, you get an Embassy letter if you renew a UK passport in Thailand but if you do it in the U.K. you don't. She won't get a letter in Laos, but hopefully that won't be an issue.
When I moved to a new condo, I didn't send off the TM28 form to Immigration until about 3 months after I had moved in. There was no issue; they just returned the slip.