How well can triglycerides be resolved using TLC? The only part of triglycerides that significantly interacts with a TLC plate are the ester moieties which are present in all triglycerides. Other than that, they do not differ much, except in mass (dependent of the chain lenght of FAs) and shape (saturation degree of FAs). How much do these differences alter the interactions causing the resolution?
If you work with normal phase TLC, you may lower the polarity of your mobile phase, and instead of mixing ethyl acetate with petrol ether, you may give diethyl ether / petrol ether (like 5:95, v/v) a try.

Some of the TLC manufactures even provide databases, pointing towards publications were compounds of interest were successfully separated.  Often, these references refer to a separation on TLC-scale.  CAMAG's CCBS Database is one noteworthy example.