Where are you seeing £500 return fares between LHR and MAN?

What does it cost to book MAN-LHR-SYD on the QR website? She’d be able to have her bags checked through and the T5-T3 airside connection is relatively pain few.

I think you’ve made a big mistake in booking this as separate trips. Bags won’t be through checked and she has no protections if there are delays and she misses any of the flights.