There's a few ways to do this, though service conductors cannot pass through another building, so all the methods will have to avoid that.
One option would be to install a service disconnect, and then branch from that to the panels.
With this method, you'll handle all the grounding and bonding of the neutral in the disconnect. So you'll install 4 wire feeders from the disconnect to each panel, and keep the neutral isolated in each panel.
Another option is to use the first panel as the service disconnect, and feed the second panel from the first.
With this method, you'll handle all the grounding and bonding of the neutral in the first panel. So you'll feed the second panel with a 4 wire feeder, and isolate the neutral in the second panel.
With is approach, the first panel will have to be rated to handle the total current of both panels.
In all cases, you're going to need properly sized feeders, and a grounding electrode system for each building.
The scope of this project is far too vast for a short answer format site, such as this. I've given a high-level overview of how you might approach the project. For a more detailed plan, please contact a local licensed Electrician.
You haven't stated much about the subpanel in the pool building, and it would be nice to have 100A in the garage given the plans you have, and the plans automakers have for future vehicles.
So I would simply extend the pool circuit as 100A. You can do that with lugging only - you won't need to add a bulky circuit breaker in the potentially small pool panel, since the 100A main panel breaker feeding the pool will also protect the run to the garage, being all 100A.
100A feeder is typically #1 Aluminum, unless you own a copper mine, in which case #3 copper will suffice. I'm not a fan of copper because most splice lugs and subpanel lugs are zinc plated aluminum, and why introduce dissimilar metals and pay more for the privilege?
On the garage panel, I see a need for at least 14 spaces (assuming you graduate to 240V compressor, table saw and welder, plus 4 120V circuits plus two 240V EV chargers. The worst mistake you can make is short yourself on breaker spaces, so think big - like 30 spaces. You do need a shutoff switch in the garage subpanel, and usually people just select main-breaker panels but the amp rating doesn't matter. 30 space panels typically have 150-200A main breakers, which is fine.
Never rely on 'double-stuff' breakers to solve full-panel problems. Most breakers these days need to be AFCI and/or GFCI, and those are simply not available in double-stuff.
It would sure be nice if the pool panel had "thru lugs" for onward connection to the garage. Think about changing the pool panel for one with thru lugs.
Best Answer
Yes you can...
Your configuration is anticipated by NEC 230.40 Exception 3:
but you're making your life harder than it needs to be
Your problem, though, will be jamming that outsized URD cable down the conduit. It has one more wire in it than you need (since you haven't hit a service disconnecting means yet, you don't need to separate ground from neutral for this run, and the panel in the garage will be a main panel), and running cables through conduits is a pain in the rump as a general rule, in addition to being rather wasteful of conduit fill.
Instead, I'd suggest running a trio of #6 copper THHN/THWNs (black, black, white) through a fat conduit (2" Schedule 80 PVC is what I'd use in your shoes). This makes upgrading to a bigger service to the garage easy (compared to digging up a direct bury cable or pulling wires out of an overstuffed conduit), and also won't leave you tearing your hair out trying to get a reliable termination on AA-1350 (yes, URD is still "old tech" aluminum) wires.
Last but not least
Since you are running to a separate structure, you'll need to put in a grounding electrode system at the garage (2 rods 8' apart, with 6AWG bare copper going rod-rod-panel, always works). This is needed to make sure that a nearby lightning strike doesn't completely fry the contents of the garage.