Should I use SER or URD cable for a 100 amp sub-panel?
SER cable isn’t legal underground, so cross that off the list.
URD also called Mobile Home feeder, comes in 3-wire or 4-wire, so it’s an option.  It’s legal for direct burial underground, but not for use indoors without conduit as if it was Romex or something.
So the real question is, what happens at the ends of the conduit?  Does the conduit go straight into the panels at both ends? Or does it just sorta end, and then ??? to get over to the panel?   I do not recommend the latter, as that ??? can get rather messy with wires this large.
If it’s conduit all the way
Then don’t use cable.  Because the wires are bound to each other, cable is excessively stiff and a real pain to “pull”.   You can buy individual wires, either THWN or XHHW.  (All THWN is dual-rated THHN).  You simply buy three full-size wires for hots and neutral, and one appropriately ground-sized wire for the ground.
Note that URD is simply THHN or XHHW wires glued together.  If your conduit is continuous, then gluing the wires together is bad, and works against you.  Get the wires individually.
You need #1 Al. Do you need a wire size bump?
Voltage drop is proportional to actual load, and cannot see the number on the breaker handle. Therefore we do not calculate voltage drop based on breaker trip.  We calculate it based on the actual, expected, or permitted load on the wires.  For instance you’re only allowed to plan for 80A on a 100A circuit, so you’d never, ever calculate voltage drop based on 100A. Never!
At less than 180’, I don’t even bother crunching the numbers to see if a wire size bump is worthwhile. It’s not.  So you’re right on the cusp. Anyway, we don’t do wire size bumps for distance. We do them for distance and load. So let me ask - how much thinking did you do about loads?

Did you sort-of “arm-wave it” like “meh, everybody gets 100A, it’s a common size”?  Or
was there a gory-details load calc like “47A compressor, 23A plasma cutter, blah blah, need to provision 93A” sort of thing?

In short, if it’s the second one, and you’re close, I’d do the bump to 1/0 Al wire.  Otherwise fuggedaboutit, just stick with #1 Al.
If you bump hots, bump ground too..   #1 Al maxes out at 100A, and that means a #8Cu / #6Al ground is sufficient.  However, if you do a wire size bump to 1/0, that maxes out at 125A, and that means you MUST have a #6Cu/#4Al ground.  When you bump the hots, bumping the ground also is mandatory per Code.  That’s because ground wires have voltage drop too, and theirs is worse, because they only carry fault current!
Don’t “Nanny Breaker” yourself.  If you decide on a wire size bump to 1/0 AL, you might as well use the 125A breaker that you are entitled to.  That way, you can the entire 125A of your feeder on the occasions when you do need it and are willing to “endure” the “scary, terrible” 3.7% voltage drop, woo woo.  You don’t need a “100A nanny breaker” to protect yourself from voltage drop.  Unless you are in Canada, because they say you do.
Did we mention BIG panel?  Buying extra spaces at install time is extremely cheap. Adding spaces after you run out is extremely expensive.  As such, we really like to see people splurge on excessively sized panels (in terms of numbers of spaces).  If a 125A feed breaker seems like a buzzkill because your panel is only 100A, that implies a too-small panel. Take it out and swap it now, while it’s still super easy to do.  That’s one mistake NOT to double-down on.