Utility peak data does not work
You're looking to use peak data for a safety calculation. The problem is, the utility does not collect peak data, at all. What they collect is "average within a sampling period". That's good enough for their purposes, which is about tariffs - certain billing plans charge based on peak. They also care about transformer sizing, but transformers are physically very heavy and liquid-cooled with enormous thermal mass, so they take quite a long time to overheat (compared with your electrical panel etc. which can melt in minutes).
If you run a tankless water heater for 3 minutes before top of the hour and 5 minutes after the top of the hour, the two 30 minute periods will indicate "15 and 25 amp peaks" even though you actually pulled 150A for 8 minutes. Yet, by "peak logic" that'd be fine on a 60A panel. No, it wouldn't!!! That data is complete garbage for our purposes.
The proper way to develop this data is a Load Calculation. NEC doesn't publish that as a form, but some AHJs (permit issuers/inspectors) have done us the courtesy, and this one is easy-to-follow and accurate to NEC 220.82 for dwellings.
Note line 2 is only kitchen general-use receptacle circuits, and line 3 already covers a washer and 120V dryer. Lines 1-3 cover all casual plug-in loads not fixed in place, so no need to account for TV, coffeemaker, table saw, etc.
"100A subpanel" doesn't actually mean that
People throw around "100A subpanel" like the Britsh throw around "Hoover". It's inaccurate in a couple of ways. First, the subpanel's rating are like tire speed ratings on your car: if it says 112 MPH, that doesn't mean you've been driving wrong all this time LOL, it's a redline never-exceed maximum. Always buy a subpanel with plenty of breaker spaces for future needs, regardless of its amp rating (just like you'll buy the tire you like the most, without giving a darn whether it's 112 or 130 MPH). Nobody ever said "HELP, I need to add a load and I have plenty of breaker spaces!" Spaces are cheap.
I've never seen someone wanting a 100A subpanel who actually did the sharp-pencil math to say "I need 100A and not 90A". So we're just aiming in a general direction, really. But that's fine; future expansion is a thing that happens! You might want an EV charging spot down there one day.
The "100A subpanel" doesn't require 100A of allocation; what matters is the loads on it. You run a Load Calculation on those loads alone to determine minimum size for feeder and subpanel. Then you add it to the house's Load Calculation to assure these new loads will fit in the service.
Applying 220.82, I see (conservatively) 12,000W of hot tub, 1500W x 4 for receptacle circuits giving 18,000 watts. The 40% fold-down knocks us to 13,600 watts, and we add 2000 x 0.65 = 1300 watts for heating, giving 14,900 watts or 62 amps on the Load Calc.
Let's have a sidebar about heating. Read the instructions on a plug-in space heater. It specifically says it's not for primary heating and it's not to be run unattended, because they are too dangerous. Using it as primary heating will cause your problems with your fire insurance claim and create liability for you. So toss out that foolish notion, and install an electric heater actually made for the purpose of primary heating, such as a Cadet baseboard. They barely cost more than space heaters - actually they are much cheaper, since they last 40 years instead of barely a season. So I'm penciling in 2000W, a common Cadet size, though they make them from 500-1500 watts also.
Wire length and size
We don't have superconductors in the approved electrical parts catalog yet. So we have to deal with wire resistance, and that means voltage drop. On a 240V circuit over about 150 feet, you have to break out the voltage drop calculator (although you can also break out the sharp pencil and look up tables of wire resistance, Ohm's Law and Watt's Law and all that jazz, if you really want to).
To use a calculator correctly, you have to override the wire salesman's defaults. Flip wire type to aluminum. Use true length and voltage. Raise voltage drop somewhat as 3% is a suggestion (except in Canada) and that number would only happen when the panel is maxed out. Use your calculated amps, and never more than 80% of breaker; never use breaker trip).
Your estimate of 2 AWG missed by a mile (1.61 kilometers). I get 4.08% at 3/0 AWG. Or with the far more readily available 4/0 AWG, 3.34%.
The /0's are because wire sizes go 4, 3, 2, 1, 0, 00, 000, 0000. Instead of writing 000 they write 3/0. (not really sure how that saves any ink lol). This is pronounced "three-ought".
This large wire will require costly Polaris connectors at the supply end to adapt to your <=125A breaker. On the subpanel end, honestly, the cheapest way to get 4/0 rated lugs on a subpanel is choose a 200A subpanel in the first place, remember our conversation about "spaces matter, and amp rating is only a number".
Unfortunately the cost of this will not be trivial. Another option here is transformers to step up voltage to a higher intermediate voltage for transmission. This needs to be installed with great care and competence.
