PET is preventing the bonding of the second layer of PE; as you suggest. Maybe, the boding could be increase if you rough the surface of the 1st laminate. Let me know your results.

I think, your source of problem is surface resistivity.

If you want to make a wet lamination, notice my below explanation. You know, the wet lamination is performed with 2 ways. One is solvent based and the other solvent-free.

With solventless or solvent based lamination, It doesnt matter.

The surface energy of PE must be minimum 34 dyne/cm. If you dont use corona treated PE, you can not perform the lamination. Because naturaly PE doenst have enough surface energy for lamination. Because the glue goes into the this surface. (But, PET already have surface energy for lamination naturally due to the molecular structure. But the situation is not about the PET)

PET, PE, OPP, PVC etc. ıt doesnt matter the type of substance. If you gain good adhesion between 2 laminated structure, you must use corona traeted PE (or pvc, pet, pp....).

Well, the answer to your question (problem) is stated; low energy surface of PET substrate.

Now, if you want to make the adhesion then you need to modify (denaturalize) the surface substrate as using laser beam, electrical discharge (corona), or making holes in the substrate.

Please, let us to know your thoughts please.