It's not the "Irish Royal coat of Arms", it is the coat of arms of the United Kingdom. It was adopted in 1837, which sets a limit on age of chair.

See http://en.wikipedia.org/wiki/Royal_coat_of_arms_of_the_United_Kingdom for an example

That style is often called a "hall chair" or "reception chair"

http://www.chairblog.eu/2008/08/04/a-pair-of-early-victorian-mahogany-hall-chairs/ has similarities in the legs.

the period seems to be correctly identified, but the value will have changed.

Where did your mother get the chair? If it has a solid "provenance" (history of who owned it and where it has been) it's worth more.

If you can get a better closeup of the arms, I might be able to narrow the possible sources of the chair for you. There are differences in the details depending on who is using them.

As Victoria came to the throne in 1837 (changing the Royal Coat of Arms to remove the Hanoverian escutcheon, to which as a female she was not entitled), anything after 1837 would be Early Victorian, not Georgian.