VRT doesn't have to be paid, you are only arguing about the principle and €20 for the number plates.
The op's wife cannot satisfy this condition and therefore imo is definitely not liable for VRT.
Even without the above example the woman is living outside the state, working outside the state, paying taxes outside the state and visits Ireland for a day or two per week. Anyone thinking the above means she is a resident of the state is deluded.
Also OP, if she doesn't already have one tell her to get a UK licence. Its easy to change over and with a UK licence and up to date UK tax it will get her through 99% of checkpoints.