JMO, as I stated before, this was no act. He really didn't know Lori very well when he married her, and with all the burner phones, probably did not know her current number off the top of his head.
All good preppers and Constitutionalists know that you do not have to answer these kinds of random questions from police because you have the right to remain silent. There are numerous You Tube videos put out by lawyers explaining why you should never talk to the police. You only implicate yourself.
IMO, he may not have known at that moment that the children were dead, only that there was a "custody battle". Not a popular view, I know, but still possible.