If you add your mum as a third pax, they will not use her voucher, neither can you book and then retrospectively apply a voucher. You can obviously book for 2 and then book via her account for her but they would be separate bookings.

I would think the only way to get you all on one booking would be to call, if it is even possible. You can be a third party nominee on your mum's account if she is not there to speak to them in person.