Your wires are undersized for Full 100 Amps unless you use #2 copper, and #2 copper will cost a LOT. (#3 will actually work, but good luck finding that in stock, and it will still cost hugely)
You can do 90A on 2-2-2-4 aluminum "Mobile home feeder" which pulls just fine in 1-1/4" conduit and is very affordable. You can't put a 100 amp breaker on the input of that, though.
Price it out, calculate your actual loads, and ask yourself if the extra 10A is really worth the expense. The panel on the far end can be 100, or even 200 amps (200 amps usually comes with more breaker spaces, which are good to have) but the feed to the wire needs to be limited to 90A unless it's #2#2 #3 copper.
If you can find the unicorns (odd wire sizes not commonly stocked,) 1-1-1-3 Aluminum is rated for 100A and just fits in 1-1/4" schedule 40 (but not schedule 80) - the trick with 2-2-2-4 is that it's a dead common bulk commodity, which is not the case with three #1's and a #3.