Upvote:4
The answer is NO for several reasons.
Baggage allotment is per ticketed passenger. Your father's allotment will not be available if he does not check in, because he would be a "no show" not a "passenger" on that flight. For the same reason his seat would not be available either for your mother to have more room.
Secondly, since you are looking at the return flight to use the allotment, when your father is a no show for the first flight the return booking would be cancelled, so there would be no allotment to even be considered.
Upvote:4
In some cases it is necessary to book an extra seat, e.g. for very big stuff that needs to go as hand luggage, e.g. music instruments like a classical bass. You could try and ask the airline, if the seat you originally booked for your father can be changed to/used as an extra seat by your mother.
Rebooking the seat to become an extra seat might add a fee. Also your airline might have a strict policy on luggage, e.g. because they doubt your mother can handle the number of luggage pieces.
In any case, "ask the airline" is certainly the correct answer. In the worst case, they say "no".