When she checks in she should use her Thai passport as that is the easiest for entry to Thailand. Use this name on the ticket. Then go through UK immigration with UK passport.
You need to book a connecting flight so you can stay airside and not go through immigration. It may cost a little more but you can avoid all the Thai Pass crap.
Visas can only be obtained out of Thailand with the exception of a 90 day O visa based in retirement, marriage,etc. You cannot get a tourist visa inside Thailand.