Wasted space is not your friend
According to the 2017 NEC, a 1.5" Schedule 80 PVC conduit has 442 mm2 of usable fill. Four 2AWG Al RHH/RHW/USE-2 concentric stranded conductors (the worst case for fill) take up 112.9 mm2 apiece for a total of 451.6 mm2. This is too much for 1.5" PVC, and would explain why you are having so much trouble.
So, take those wires back and get a more compact set
The rub is that the RHH/RHW wire specification is very old, dating back to when natural rubber was the insulation material we were all stuck with, and calls for very thick insulation as a result. Newer wire specifications, like the THWN commonly used for small gauge wires or the XHHW-2 used for today's large gauge wiring, use more sophisticated insulating materials (PVC/nylon for THWN, XLPE aka the same stuff PEX plumbing is made of for XHHW-2) and thus can use thinner insulation layers, letting you get more wire into the space available.
Furthermore, today's large gauge aluminum alloy conductors are compact stranded, further increasing the amount of conductive material that fits into a given area by removing many of the air gaps between strands present in concentric stranded wires. This means that your best option here is to take those 2AWG aluminum wires (or the 2AWG quadruplex) back to where you bought them from, go to your local supply house, and get wires that use the space you have better. This also gives you the chance to downsize the ground wire and use a bare wire for that function, as a 2AWG aluminum ground wire is larger than neecessary for a 70A, or even a 125A, feeder circuit.
In particular, a set of 3 1/0 (!) compact stranded aluminum wires with XHHW-2 insulation will carry 125A (!!) to your shed, while using 102.6 mm2 of fill apiece for a total fill so far of 307.8 mm2. To this, we add a 6AWG bare copper ground conductor (this is the minimum size required for a 125A circuit by Table 250.122), which takes up a mere 13.3 mm2 of additional fill. The resulting total fill of 321.1 mm2 takes up a mere three-quarters of the 442 mm2 available fill in a 1.5" Schedule 80 PVC conduit, and gives you almost twice the 70A you desire while you are at it!
If that is too pricey for your tastes, 2AWG compact stranded aluminum XHHW-2 will get you your 70A at merely a few dollars more than the RHH/RHW/USE-2 conductors you were using, while taking up a mere 65.61 mm2 per conductor, or 196.83 mm2 before we add the 8.37 mm2 of an 8AWG bare copper ground (suitable for 70A as per table 250.122) to get a total fill of 205.2 mm2. This means that with the correct wire, you can run 70A through a 1.5" PVC conduit while using less than half of the available fill area!
If returning the existing #2 aluminum is not an option...
If returning your existing #2 aluminum wires is not an option, then you can use them for your hots and neutral, yielding 338.7 mm2 of fill so far, and then add an 8AWG bare copper for the ground wire, which adds 8.4 mm2 of fill for a total of 347.1 mm2 of fill. While this is more fill than necessary for this application, this does still fit into your 1.5" PVC conduit, and is an option if you can't return the existing wires for some reason or another.
Go BIG or go home!
While we are shopping for bigger and better parts for your run, let us not forget the subpanel. Many people skimp on subpanel spaces to save a few dollars now, but this is penny-wise and pound-foolish in the long run, as it is quite expensive to replace a panel down the road compared to the minor extra cost ($80 vs. $40) of a larger panel right now. As a result of this, and the fact that your outbuilding needs a main shutoff switch at the structure to conform with NEC 225.31 and 225.32, picking up a 24- or 30-space, 125A, main breaker panel while you are buying the new wires is a good idea, even if you will only use a few of those spaces right now.
TORQUE ALL LUGS TO SPEC (so your electrical installation doesn't have to make unexpected pit stops)
The 2017 NEC added a requirement in 110.14(D) that all terminations must be torqued to the specification marked on the equipment with a calibrated torque tool (wrench or screwdriver); for the torques used for light-duty residential equipment, a torque wrench marked in inch-pounds is adequate. Even if your jurisdiction does not enforce this, it is still a good idea especially with aluminum wire, as aluminum wires are less forgiving of termination mistorquing than copper wires are, and you don't want your hard work doing worse things to you than what Greg Biffle's infamous lugnuts did to him, right?