Choosing AC-AC PSU spec
You're probably using the wrong term. You've got a 12 V AC transformer rather than a PSU which usually means a lot more than just a transformer.
You can clear some of your confusion by doing the power calculations.

Transformer rating: 12 V × 1.6 A = 19.2 W.
Output required: (12 V × 1.3 A) + (12 V × 0.8 A) = 25.2 W.

The problem should be clear by now - and we haven't started to look at power lost to rectification and voltage regulation. If you're doing this with linear regulators you might be looking at another 25% to 40% power loss.
You need more iron and copper! Or get a suitable switched-mode power supply which will be smaller, lighter and much more efficient.