Can my mum travel domestically in Thailand with an expired visa, and what are the options for extending it in Krabi?

Recommend to border bounce before visa is expired(that is tomorrow). Since you want to go to Krabi, border bounce to Padang besar is not bad at all. Although it is a little long ride but if you arrive Krabi in the morning it is doable in one day.

If you are overstay, there is a chance to get caught. And when you get caught in other place that is not Bangkok, that mean you will be sent to stay in police station jail to wait to go to court that also will open on 18, then will be under detained and sent to Bangkok before be able to be deported. And believe me, the cost of this process officially and unofficially is as high as the price of your going home ticket plus you may have to buy new ticket since this process take long time and not finish before 22. Not mentioned 5 years blacklist. It is not worth risking.

Don't the check in counters check foreign passports for visas and stamps, even for domestic travel?? Chai mai?

I'd a border bounce straight away. Not taking any chances. It's a wasted day, but you're one the save side!

if she doesn't care about coming back to thailand then she can take the risk of overstay otherwise I'd do a border bounce tomorrow...

If she is caught on overstay, and not on her way to the airport, she will be arrested and held until she is deported at her expense, and banned from returning for 5 years. She can not get another extension. It is up to immigration whether they detain her, or give her a 7 days to exit the country stamp. This can get serious if she doesn't go to immigration on the 18th. Not the 19th, but the 18th. Or, just gamble, and hope she makes it until her flight out, but get there about an hour earlier than you normally would so she can pay her bt500 a day fine, and get an overstay stamp. If she is caught she gets detained and deported, and banned. During this holiday period is where immigration actively seeks overstayers, with much of it done easily through TM30 filings.

After 16 april, every officer can catch her. If you fly domestic the officers at the passport check , may or may not see the expired stamp and can catch her.

Safe way , you dont fly to Krabi, you fly to Phnom Penh or maybe Laos , stay there 1-2 days and then fly back to Bkk to catch the flight home

I think the answer is no

You mention her extension will expire ? You do understand on visa and visa exempt you can only extend once so if what you are saying she already extended once she can not do it again.

What visa is she on when arrival into Thailand and has she actually done one extension already ?

If she doesn’t get caught she’ll just pay 500 baht a day overstay if two days or more plus the infamous overstay stamp in her passport if you go to immigration the day it opens no fine but still overstay with immigration being closed as a reason neither one is serious but just not good to ever overstay sorry just read her extension is up she cannot get another extension unless medical or possibly get the 7 day exit stamp good luck and next time plan ahead

Visa/extension status will not affect the ability to fly domestically in Thailand

Go to Krabi immigration, but not open until 18th. Or risk overstay 500 bt a day at the airport. Immigration office should not charge for overstay due to closure. However if already done 1 30 day extension then you cannot get another. Immigration can be asked for 7 day " must leave" stamp.

You don't say what sort of visa (if any) your mum has so difficult to answer but assuming she's either visa exempt or on a tourist visa she can only extend this one time and you imply she has already done this so the only option would be to do a border bounce. All immigration offices are closed until the 18th, she might be able to get an extension refused stamp which gives her 7 days to get out of the country when they reopen but they don't have to give this, make sure to take the flight details with you. I wouldn't recommend going on overstay beyond the 18th as if she's caught on overstay before she gets to the airport she could be deported.