Could the "cover" in question refer to some sort of baby wearing device?
I wonder if they arrested the dad for leverage to check out his story. Rather than being a suspect, maybe they wanted to make sure that he wasn't leaving out information due to fear. Maybe they just wanted to question the parents separately and took advantage of the outstanding warrant.
While I understand the drug debt line of thinking, he was arrested on pot charges, not crack or heroin. I don't think you end up in the same kind of debt over marijuana. At least, it's much more difficult because there's not the same sort of massive physical illness associated with withdrawal. Also, at the risk of sounding glib, it's pot. It's legal in 2 states now recreationally. Plenty of good upstanding parents use marijuana as an alternative to alcohol, pain meds or psych meds.
(Yeah, I know. I'm a Pollyanna. I always look for the good in people. I've been called the most optimistic jaded person people have ever met. But for me, the jury is definitely still out.)