How to separate two liquids with both having the same properties?
Typical vegetable oils are not just one chemical compound, but a mixture (after removing everything that is not) of glyceride triesters. The chance that there is some overlap between your two oils is big, so the answer to your immediate questions likely is no, completely impossible.

Even if there is no overlap in the chemical composition, you would probably still have to separate the oil mixture into all its components, and then know how to mix them together again to get the original two oils.

The latter is possible, of course, with a reasonable analytical effort, the former is close to impossible to perform on a macroscopic sample. A GC(-MS) can easily separate (and identify) the compounds, but that's a few billion molecules or so. Doing liquid column chromatography would be very tricky, with any reasonable apparative effort would give you a few milligrams of each compound, and perhaps there are still a few you can't separate.

Distillation is impossible (boiling points are high and too similar), fractionation by crystallisation would only work well for some of the triglycerides, etc. All in all it's a bad mess. Don't mix two oils and try to separate them afterwards. ;-)