Uogrades will not happen because mum is in First. Otherwise that would be one hell of a top tip to get a free F ticket: only one of the travellers will have to buy an F ticket. No chance in hell.
Upgrades are ONLY given when the flight is oversold and then by status and fare class. So the Platinum member will be upgraded first, gold second, etc. They will even split up couples if only one has status.
Next a 2 class upgrade (Y to F) is not allowed per the airlines policy. So "I would like to sit next to my mother" is not even possible. Unless she is willing to downgrade to C, but it looks like your mother likes to spend some quiet time in First alone...
So, in summary: don't get your hopes up. You may be upgraded to business IF
you are Platinum or Gold AND
you are on a full fare Y ticket AND
the flight is oversold. Otherwise: enjoy Y!
Edit: upgrades almost ALWAYS happen at the gate and never ever ask for one. The best way of not getting an upgrade is requesting an upgrade. If you are very lucky your mother can try (if F is very empty for instance) to ask the purser on board if you can join her. That is not technically an upgrade, since you are in Y for take off and landing and your ticket still is Y. She needs to do some serious grovelling though and considering she bought you a Y... Chances are slimmer if she is travelling on an award ticket by the way.
[Edited 2008-06-24 03:38:54]