To add to my earlier post, have a look at Austlii I suggest. The link is
There have been cases in the MRT where Parents have entered Australia on tourist-visas but have then tried to apply for some sort of Family Residence (AO) visa. I haven't a clue what this is, and it may be a type of visa that cannot still be obtained. Anyhow, the Parents seemed to have been granted Bridging Visas until the whole thing could be thrashed out in the MRT. There have also been cases where people have been refused tourist-visas and-or refused entry because DIMA has not been satisfied that tourism was the real purpose of the visit.
If anyone has tried the proposal which you have in mind, and DIMA has baulked, the MRT cases might well reveal what happened in the end if you search Austlii. In your shoes, I would certainly search it to see whether you can discover anything that might give you any leads to follow up on and-or questions to ask of an experienced and reputable Migration Agent before you decide what to do.
The other thing I did not mention last night, to avoid confusion, is Condition 8503. If your mother is in Australia on a tourist-visa and Condition 8503 has been imposed, she would not be able to make a valid application for any sort of Parent visa from onshore in Australia. My mother is subject to Condition 8503, which is what forced me to examine the idea of tackling this from the "other way around" if you like. OK, Mum could not make a valid application for a CP visa from within Australia. Fair enough. Could she, instead, make an offshore application for the CP visa and then use another tourist-visa off the back of it, in order to allow her to be able to spend most of the processing period for the CP visa in Australia rather than here? I found that she could. The DIMA website specifically draws attention to this possibility.
(I would send you the link to the relevant page, but I found it by sheer chance, by following link after link, and I cannot now remember the sequence in order to get back to it. In the end, I went through the website like a dose of salts, printing every page that looked remotely relevant, trapping the whole lot in a large lever-arch file, and using a marker pen to highlight all the bits that seemed useful! Not at all fair on the trees, but better than repeatedly getting lost in that website, I found!)
So I tried this suggestion of DIMA's, found that it works very well, and I think it is actually a much better option for the Parent than getting involved with a Bridging Visa instead because I reckon that when the Parent is getting on a bit in years, the availability of Medicare is an important consideration. Also, it avoids all and any possible arguments about anything, because it is the solution that DIMA themselves recommend on their own website, so they can have no possible quarrel with the idea.
It is working very well for us, so I hope that you will give it sympathetic consideration on behalf of your own mother too.