Is chuig also right?
"Thúg an dlíodoir fógra chuig mo mháthair"
You use chuig (or chun) with tabhair to mean something like "take to". The FGB example given is Tabhair chugam anseo é ("Bring it here to me")
Chuig (or chun) is used when the emphasis is on the motion of “to”; do is used when the emphasis is on the purpose of “to”.
is " a mo mhathair " not acceptable ?
There are nine different entries for a in the dictionary - none of them allow for "a mó mháthair".