As long as you can show that you have enough money to pay for the whole trip (and you said you were only going for 2 weeks, so it shouldn't be too expensive) it should be fine. You have kids in school in Thailand, so include proof of this and any letters from the schools giving you permission to take them out of school for the trip to the UK. There is no requirement for your wife to be working, if she's a housewife!
You don't post it. Once the form is complete and you've paid, you set up an appointment in Bangkok (@ VFS) to hand it in, together with the supporting evidence, and for the biometrics. Then it's about a week before you get the email to say the passport can be collected, either with the visa inside or a notice of refusal.
Make sure you enclose a copy of your permission to stay in Thailand - i.e. work permit/extension, retirement/marriage extension - and details of your kids' schooling in Thailand. I doubt you will have any problem getting the visa.
All UK visas are for 6 months (multiple entry). However, on the application she will need to say how long she plans to stay in the UK. If she says "6 months" she will need to explain how she can be away from Thailand for so long. Very few Thais can get a 6 month holiday from work.
VFS is the drop-off centre for UK visa applications. They will check the documentation and forward it to the UK Embassy. You will also need to collect your wife's passport from there. Biometrics include a photo, and other information (retina) which is to verify your wife's identity and store it.