Unless it's changed when I wasn't looking, visitors can stay in the UK for up to 6 months rather than 3. I understand that it isn't a given that a passport will be stamped for 6 months rather than the length of time till a return ticket.
I agree with what Shandy said as far as what you need to show the IO, but if your Mom is worried she can apply ahead of time for a visitor's visa. Not required, but it does give peace of mind.