No train, but there are AC buses from both airports (Suvarnabhumi and DMK) those are pretty comfortable and does the job. Or you can take private taxi.

@Stuart ********

ohk thanks that clarifies

@Stuart ********

ok basically there is single queue for immigration whether one has any type of Visa.

@Stuart ********

sorry forgot to mention in my post, i am looking for tourist visa. My main concern in wait line in immigration, will it be came queue as other who take VoA or different.

So even i am in process to understand visa procedure and i found this to be guidelines -

And this clearly states you have to book an appointment to give your biometric and photo taken which will be used to issue a visa. So unfortunately it looks like your mom has to visit the center in person, nahi to you get 15 days VoA which i don't think serves your purpose.

VFS is pretty much the sole agency appointed by Thailand for Visa purpose.