Asymmetric handling problem from blown shock?

[ST1G]

I think you have that backwards...when turning left, weight transfers to the right.

The rear tires are old (fronts look okay), size is 195/65R14.

Opps. you're right. Sorry.

My guess would be tires. I have some old 195/60/14's on my e30 with sport springs and good shocks and it handles really poorly. When I had new 205/40/17's on the car it handled really well. I defiantly think it's the tires and the blown shocks causing the issue. The other shocks are probably in bad shape too even if it's not as evident.

[Young Version]

Sounds like you have a blown left rear shock. When you turn left the mass of the car is shifted onto the left side.

What size are the tires and how old are they?

I think you have that backwards...when turning left, weight transfers to the right. I definitely have a blown left shock.

The rear tires are old (fronts look okay), size is 195/60R14.

[ST1G]

Sounds like you have a blown left rear shock. When you turn left the mass of the car is shifted onto the left side.

What size are the tires and how old are they?

[Young Version]

I just picked up an e30 a couple weeks ago and I've put in a few hundred miles since then. Here are the specs:
-89 325is, manual, 3.73 LSD, upgraded cam and chip.
-Stock basketweaves with Falken ZE912s up front and Uniroyal Tiger Paws out back. The rear tires are very dry and have a decent amount of wear from camber.
-Suspension is all stock except for Tokico blue shocks and H&R Sport springs. The left rear shock is blown, and I intend to replace all four shocks with Bilstein Sports. All the bushings are original and desperately need to be replaced.

The car has fairly low limits right now, as I expected, but the rear gets REALLY loose during left turns. I'm forced to corner slower than I do in my wife's Prius, because I really don't need to be getting sideways in intersections.

My immediate thought was that something must be very wrong with the suspension on the right side, but a friend tipped me off to the possibility that the cause could be my blown shock not rebounding as it should.

I'm planning to replace tires, bushings, and shocks before driving the car hard, but in the meantime, does anyone have any idea what could be causing this?