tl;dr: Since your living situation has a high likelihood of changing within a few years, I'd recommend *not* purchasing a home now.
Wow, your situation is certainly one I've not seen here before. That said, I have a sibling who found herself in a similar situation several years ago, albeit at a younger age. There are a lot of moving parts here--alimony now, alimony in two years, potential earned income now, cash ready to invest, wanting to buy a home, etc. Here are a few thoughts:
--It will be hard. My sibling had also been a SAHP for many years, and basically had to start from scratch. It will be hard. Get used to that idea.
--It appears that all of your options assume a home purchase with cash. There are at least two other options which may be more helpful: A) rent, or B) buy a house with 20% down. If you take option B, you'd only have to put down $140k, leaving you with $710k to invest, although your income would then also have to cover a mortgage payment.
--I'm a little confused. You mentioned that your expected lean-FIRE spending is $30k/year, assuming a paid-off house. But your actual expenses only add up to (housing + $2,020)/month, which is substantially less. And once the kids are off to college, I can only imagine your grocery budget will plunge, driving your spend even lower. Are you expecting home-related expenses to make up the gap?
--You are four years from empty-nesterhood. Since your lifestyle is likely to change dramatically at that point, I'd hold off on purchasing a home just yet.
--You also just moved across the country, and you have a place to live for the time being, so I would suggest you not rush into also buying a home. You have enough major transitions to deal with already.
--If you start working now, does your earned income going forward get you credits toward social security? You have to have 10 years' worth of credits in order to get anything out. I ran to the SS quick calculator, and if you worked from now until age 65, at $50k/year, you would be eligible for about $12k/year in SSI at age 65.
--You need to build yourself a spreadsheet. Each row is a year, and the columns show your projected earnings, savings, and spending. In addition, cFIREsim is an excellent tool that can let you add all sorts of adjustments to income and spending.
Because your income will vary dramatically, but only over the next four years, But let's run through a couple of scenarios. These all assume 7% growth after inflation, so treat them as only a starting point
Scenario A: Buy a $700k house with cash, $30k/year spending, invest the remaining $150k
You start with $380k. You work and earn $40k/year after taxes.
Years 1-2: You can invest ($76k+$40k-$30k) = $86k
Years 3-4: You can invest ($38k+$40k-$30k) = $48k
At this point, you'd have right about $750k saved up--enough to cover your $30k/year expenses. You could retire at this point. Or, you could continue working and allow your stash to grow.
Scenario B: Put 20% down on a house, invest the rest. Work to earn $40k/year after taxes.
Principal and interest on the mortgage (4%, 30-year) would be $2700/mo, or $32,400/year. Total spending: $62k/year
Now, you start with ($710k + $233k) = $943k
Years 1-2: You can invest ($76k+$40k-$62k) = $54k
Years 3-4: You can invest ($38k+$40k-$62k) = $16k
Years 5-10: You can invest ($0k + $40k - $62k) = -22k (you start to draw down your accounts)
At age 60, you have just the right amount saved up ($1.55M) to cover your $62k/year spending
Scenario C: Stay renting the apartment, invest everything
Spending is the same as current ($48k/year)
Now, you start with $850k + $233k = $1.18M. In this scenario, this is almost enough to let you retire right now, with the 4% rule.
Years 1-2: You can invest ($76k+$40k-$48k) = $68k
Years 3-4: You can invest ($38K+$40k-$48k) = $30k
At this point, you would have $1.66MM. This gives you enough to pay for the house in cash and still have more than enough to retire. That said, home costs could have risen further in this time)
Of these three, B looks the worst. That's because a good chunk of your spending is going toward interest, plus another chunk is increasing your net worth via home equity, and it does not account for appreciation of your home
The housing industry in the US in in a bit of a perfect storm: inventory is at historic lows, demand is suddenly higher (remote work!), material costs for new construction are much higher, labor shortages and material shortages are causing all sorts of headaches. I personally expect things to settle down over the next couple years, as the shocks from covid work their way through the system, but it's going to be a rocky road.
All that said, you've stated that you're willing to relocate to be near (or at least in the same country as) your kids. Since they'll both graduate high school in the next four years, I'd suggest you hold off on purchasing a home until you have a better handle on what your life will look like. In the meantime, find a good job, save like crazy, and enjoy the time you have with your kids!
