Unless you are wealthy, there is no way to stay in nice hotels for 200 pounds a night if you are staying a month and are an average earner. You need to put expenses on top which is way beyond what most people can afford.
Serviced apartments are as expensive as hotels, and even Airbnb are expensive.
In Australia the vehicle is insured not the person, so you can add people easily online or by phone and it just means a slightly higher excess if they have an accident.
Third party insurance in Australia protects the vehicle and the people driving it against an accident against, let's say a Porshe, costing thousands to repair.You are right, the person insured need to add the OP to the vehicle, but the OP still needs to get a valid international licence. Without it, she can't drive a car, insured or not.
Regarding flights, we usually book and pay for them a year in advance (Early Birds). I don't bother with googling best deals, I go to a travel agent directly. They have the software to get the best deals possible, and some airlines have superb deals when booked early on.
The OP is looking for ways to stay close to a daughter permanently living in OZ. She's not looking for a holiday - if she has a solid relationship with DD, and time to schedule a few months in OZ, it won't cost a fortune and will love spending a few months in the Australian summer when the England the weather is the worst.
Many of us parents with kids living on the other side of the world are making it work without costing us a fortune. It takes a bit of organisation and lots of communication.