Welcome to Flyertalk and welcome to the BA Forum.
This shouldn't cause a problem. Depending on when you bought the ticket and the dates of travel, you may even get either a part refund or a voucher for some of unused ticket. It won't affect the other members of the group. Technically what you should do after flying the outbound, ring up, split the ticket so that mum is on her own, then cancel / voucher mum's ticket. It's quite straightforward for an agent to do this, just takes a few seconds. The only potentially tricky bit is if you used a companion voucher from Amex or some such when there are on paper certain requirements. But even then the system isn't that clever and people can drop out without problems.