Can my wife with both Thai and UK passports return to Thailand on a second visa exemption within two weeks?

She can book flight with the name of either passport. Just make sure to use the correct set of the name, nationality, and passport number on the passport that is used to book a flight. As long as she has a valid Thai passport, she can enter Thailand on that. She wouldn't have issue with airline if she can show a Thai passport if it's not used for booking.

And as long as she enter Thailand on a Thai passport, it's not visa-exempt entry for foreigners as she is Thai to enter. No limit on entry to Thailand for Thai nationals.

Perhaps sooner or later you may want to take the necessary steps to get your wife’s name to match on both passports. Could prevent future issues.

My kids use both Thai and UK passports but their names are exactly the same on both passports. Get that sorted and it becomes a non issue.

That said, she will have no issue arriving on a UK passport and get stamped in for 60 days.

She can book her flight in the name on her UK passport and use that to check in and board. After disembarking she can show Thai immigration her Thai passport. When leaving Thailand she can check in with her UK passport and pass through immigration with her Thai passport then swap back to her UK passport

Why doesn't she use both passports if you're unsure!

Out of UK, UK passport,

into Thailand, Thai passport.

Out of Thailand, Thai passport.

Into UK, UK passport.

Use her Thai passport for immigration to enter and leave Thailand regardless of the different names. Show the airline the name she use to book. Always carry both.

Have her use her Thai passport to enter Thailand and depart on her next trip to Thailand.

Same with her daughter if she has a Thai passport.

If the daughter has only a UK passport, she will use it for travel with her Thai Mother.