It's fly, train, or car isn't it? If there were a direct coach from Stockport, or even Manchester, that might have been acceptable in the circumstances, but there doesn't seem to be.

If you're worried about her ability to handle luggage, I'd avoid the train, and associated changes (though well within your budget, I suppose, you could do 1st class to Euston and taxi to Heathrow).

I know you're wanting to avoid different bookings, but a day before Y flight to LHR, coupled with a night in the Sofitel attached to T5 (or one of the T2/3 hotels for QF), would also come in under budget and minimise risk, outbound at least.

Otherwise, it's suck it up, or get a taxi I think.