Electrical – 3 wire sub to main panel upgrade

So, you have 8 gauge wire potentially subject to a fault current of up to 200 amps without anything tripping. You also have the neutral and ground bonded in a sub-panel (despite running separate neutral and ground wires to it, so bonding in the sub-panel is a puzzling choice in itself, as well as being a violation.) [or else possibly you have written unclearly about what you have done with the ground and neutral?]

Wrong. Just....wrong.

Pull two breakers, insert a 50 A breaker, and move the 15A circuits to the sub. And unbond/isolate the neutral and ground in the sub. Get a different/larger sub-panel if you need additional circuits (or give a long hard look at a complete panel replacement with adequate spaces in the main panel - not all that expensive if the incoming service is adequate, but attached to a panel with few spaces.)

If your panel is listed for them breakers with two separate 15A circuits in a single space breaker are another option to make space.

Ditch the URD

Underground Residential Distribution cables are really uni-taskers: all they're good for is buried residential service from the utility. Most of the commonly available ones lack a ground wire (hot/hot/neutral), and they're often made from AA-1350/EC aluminum, which is picky about proper termination.

Instead, especially since you're considering using conduit anyway, I'd use individual XHHW-2 AA-8000 alloy conductors in a generously sized schedule 80 PVC conduit -- 2" would not be at all out of place for this run. A box can be used to make the transition to SER cable once you get into the basement, or you can simply keep going with the conduit run. Make sure to leave enough access points (pull elbows, conduit bodies, boxes) to make the run practical, and use expansion fittings in aboveground PVC runs subject to temperature changes!

As to conductor sizing, 2AWG aluminum should be fine for your purposes -- voltage drop will still be acceptable even at the full 60A you propose for this feeder. Given the amount of it you'll need (over 450') and that it's large enough for phase taping to be permissible for wire identification, it may be cheapest simply to buy a full 500' spool of the stuff instead of buying it by the foot. You'll also want some 6AWG bare copper for the grounding electrode conductor at the garage, and 10AWG bare copper for the equipment grounding conductor in the feeder run.

Keep 'em separated!

Speaking of grounding, you'll need to be careful on this point. Past practice with outdoor feeders treated them like services, bonded via the neutral, but this is no longer allowed -- instead, your feeder will be a full 4-wire feeder (hot/hot/neutral/ground) with neutrals and grounds separated onto their own bars and the loadcenter's bonding screw/strap removed.

Furthermore, you'll need to provide a grounding electrode at the garage and tie that to the grounding system: a concrete-encased (Ufer) electrode is ideal, or if your garage is steel-framed, you can tie into that. If neither of those are practical, a pair of ground rods driven at least 6' apart will do the trick.

Go big, or go home!

There is no shame in getting more loadcenter than one strictly needs -- it is often cheaper now to buy a somewhat larger loadcenter up front than to replace an undersized loadcenter later. Given that, the fact you'll need a main breaker loadcenter to provide the structure with a local disconnecting means (it's OK if the subpanel main is oversize as all it needs to be is a disconnecting means), and that a NEMA 1 cabinet will suffice for going inside the garage (all the space needs is four walls with doors that close and a roof that won't leak), I'd recommend a Siemens P3030B1100CU for this application as a minimum specification -- it provides plenty of spaces for an outbuilding application (30 spaces for a 100A panel is quite a bit), and ships with all the terminal bars needed (including separate ground bars). Of course, you are more than welcome to drop a few extra bucks on a larger panel (but you'll have to go up to 200A bussing to do so, most likely) -- a 42 space/200A loadcenter would not be at all out of place here.

TORQUE ALL CONNECTIONS TO SPEC

Last but not least, get an inch-pound torque wrench and torque all breaker and panelboard lugs you are connecting to up to manufacturer specified torque when you're doing this -- it's a new Code requirement for 2017 (see 110.14(D)), and just a darn good idea from a reliability standpoint, unless you want to pull a Greg Biffle with your garage's electrical system, that is.