United's policy on "Customers requiring extra seating" can be found at http://www.united.com/web/en-US/content/travel/specialneeds/customersize/default.aspx. (It took me a while to figure out what euphemism to search for.)
A customer flying in the economy cabin who is not able to safely and
comfortably fit in a single seat is required to purchase an additional
seat for each leg of their itinerary. The second seat may be purchased
for the same fare as the original seat, provided it is purchased at
the same time. A customer who does not purchase an extra seat in
advance may be required to do so on the day of departure for the fare
level available on the day of departure. The customer may instead
choose to purchase a ticket for United First®, United Business® or
United BusinessFirst®, or elect to pay for an upgrade to a premium
cabin if there is availability to do so. United Airlines is not
required to provide additional seats or upgrades free of charge.
A customer is required to purchase an additional seat or upgrade if
they do not meet one of the following criteria:
- The customer must be able to properly attach, buckle and wear the seat belt, with one extension if necessary, whenever the seatbelt sign
is illuminated or as instructed by a crew member.*
- The customer must be able to remain seated with the seat armrest(s) down for the entirety of the flight.
- The customer must not significantly encroach upon the adjacent seating space. See our seat maps.
United will not board a customer who declines to purchase a ticket for
an additional seat or upgrade for each leg of their itinerary when
Without knowing your mother's exact size and shape, it's impossible to know whether this will be an issue, but I think it is a distinct possibility, particularly on the Q400 and CRJ-700 which are small aircraft and feel significantly less spacious (even though, according to SeatGuru, the seats are only 0.2 inches narrower than on, say, a 737).