@riccrees
I'm not personally a fan of lawyers and appeals, I feel it's an expensive option with limited chances of success. This is especially true when it occurs at airport passport control, rather than as part of an application for a visa or a residence at the immigration department, or overseas at an embassy. In the latter, there's typically a process for appealing a denial and/or rectifying any shortcomings in the application. In the former, immigration officials have pretty wide latitude to deny folks entry, and, in your son's case, it certainly seems likely that he had overstayed considerably without a valid residence visa/permit... and possibly was also working illegally during this time, even if he didn't realize it.
So, what other options are there?
Having received a ban, I doubt he can easily return to Spain in the short term. If his partner has a great job in Spain, and must stay there. they might have to plan on Skype calls for 2 years. If she has more flexibility, then she could join him in Australia... or any other country where they can both easily live/work. Places like Dubai, Turkey, and Bali spring to mind where it's pretty easy to get residence, and they can hang out for a couple of years. But this depends on their financial situation and/or whether they generate remote income.
I also see 3 other options:
(a) Residence permit in another EU country
I would suggest that they both relocate to another EU country and get legal residence there. Having a legal residence somewhere in the EU should substantially reduce the potential aggravation from immigration, and might even let you back into Spain (as a residence permit in any EU country grants you 90 days visa-free in all other EU countries). It also starts the clock on permanent residence (5 years), which is a key milestone for non-EU citizens, and allows them to stay indefinitely.
She would get hers by EU Citizen Registration (very easy), and he would get his by Family Reunification (almost as easy, except for cohabiting couples). However, it probably can't be a Schengen country because of the big overstay, so that only leaves Bulgaria, Cyprus, Ireland, Romania. If it's strictly a Spain ban, then there would be more countries to choose from.
If your son and his partner have been considering getting married, or entering into a civil partnership, then they should be aware this greatly simplifies family reunification. The EU recognizes cohabiting partners in a "durable" (more than 2 years) relationship, but the issue is which of these countries implement this, and what proof they accept for the relationship... it can be tricky. Easy is marriage cert, or proof of a civil partnership.
(b) New passport
I would suggest he "loses" his Australian passport. The new one should have a different number, and decouple him from his overstay and ban (and it should have nice blank pages if they actually stamped something nasty in the old one). I don't think Schengen Zone does fingerprints at passport control (which the USA does), but if they do it won't work.
I wouldn't lie to immigration, and if they asked me about my ban I'd tell them the truth (or a spin on it). But if it's a clean passport, they might not even ask.
This should be pretty quick, I'd guess a couple of weeks, and I'd be tempted to see if I could re-enter Spain on this one. If so, I'd try the Family Reunification again, ASAP... but make sure I actually got my TIE this time. :-)
(c) New visa
I'd want to check the ban, and whether it's for all of Schengen, or the EU, or Spain only. I'm guessing Schengen. And I'd want to check if it's a "hard" ban or not. In particular, does it stop him from getting a Schengen visa, or a Spanish residence visa? My guess is that he can't re-enter Schengen only with his passport (relying on the visa-free exemption of Australian passports). But if he gets a new visa (Schengen or Spanish) he'd be able to enter with that.
For example, your son could consider applying (at his local Spanish Embassy), for the DNV (Digital Nomad Visa) or the NLV (No Lucrativa Visa). The former needs provable income from remote work, and the latter needs provable passive income (2,500 per month) or demonstrable savings (30k). Neither of these would let him work in Spain, but they would get him back to Spain with his partner, and they can figure out their next steps, and how to change to a different residence status.
I was in a very similar situation a few years back, so I have some direct experience of the challenges of legal relocation for non-EU citizens. Back then (pre-Brexit) I was an EU citizen, while my partner is a TCN (Third Country National) from Brazil. We frequently had hassles with border control, especially as back then she didn't speak any English (as we spoke Spanish to each other). Once we got her legal residence in the EU, those hassles disappeared.
I was working in the UK, and my partner visited multiple times, and returned to our house in Germany between visits. So she had not even overstayed. However, she was denied re-entry (to the UK) after a short holiday in South Africa. Effectively, she was deported, and put on a flight back to where she flew from. And her passport had a big scary stamp put in it. Which every border control guy would spot and ask about (even when it wasn't for their country).
We had to figure where she'd go... and how/where we'd live. We both flew to Bulgaria (from different countries). I paid an immigration attorney 1,500 euros for a rental contract and two residence permits. I had mine in 2 days, and she had hers in a week. (Bulgaria is easy and cheap, and they do allow cohabiting couples. But only if they have a proof of residence in another EU country. If your son and his partner recently - within last 3 months - got their padron certificate at their local town hall, I'd tell them to grab it and fly to Sofia. If not, Bulgaria's off the table.)
Next, she went to the Brazilian Embassy in Sofia to declare she'd lost her passport, and get a new one. Shortly thereafter we repeated the residence process in Spain, without problems, so we both have residence permits for Bulgaria and Spain. A few weeks later we tried popping back to the UK to visit my family, and that was fine too.
Overall, it was pretty dramatic, and a right pain in the proverbial. It cost a chunk of cash, and I had to ditch my cushy university job in the UK. But it actually didn't take long to sort out this way, and we were not separated for more than a few weeks. And we ended up living a very nice life in Bulgaria, which we totally had not expected. Spain's great too, can't complain. :-)