Could Jane's Father Alex be the Red John?

Red John started killing 1998. We don't know where Alex was at that time. Perhaps he joined Visualize, and Stiles gave him ideas how to win his son back. Stiles always seemed to know more about Jane than just watching his TV shows. And who could tell him more about Jane than a proud or disappointed Father can?
Jane's insult over the TV, really hit Red John hard. We all expect strangers/enemy to be harsh towards us, but the biggest pain is when your family hurts you. The killing was personal, but perhaps more than we are led to believe.

Red John's letter to Jane after killing his family accuses Jane of faking his powers. Who knows the truth better than Alex?

Why did Red John paint Angela and Charlotte's toenails? Was that done to bring the attention to the hands? Pointing out that "Bite The Hand That Feeds You"

One thing I don't remember to be ever revealed is if Red John broke into Jane's house at the time of murder or was he let in? If there was no signs of forced entry then his wife knew Red John, and she must have met Alex being part of the same carnie.

He might have killed Jane's family hoping the pain will drive Jane back to him. Jane might even know that subconsciously which was reflected in the hallucination of his daughter who didn't wanted Jane to find her killer, because it might be too hard to for him to handle the truth. 

Sure, Lorelei said something about a handshake, which would make the theory ridiculous, but if she was misleading Jane to give herself time to find Red John first, then perhaps we should look at her comparison " You are just like him" and you know what they say: "Like Father Like Son" "Apple doesn't fall far from the tree" and so on so forth.