Well, considering that he's a police officer and military, he was probably fairly strict. To some folks that's abuse.

(I'd say it's a difference in parenting styles. My DH's parents were fairly strict, mine were fairly tired of raising kids, and we both love our parents and turned out perfectly okay and neither one of us would say we had a bad childhood.)
My DH actually worked with someone who took his kid and ran - we had a family court judge in our area at the time who firmly believed that children should go with the mother, no matter what. This co-worker's ex was living with a known drug dealer (as this gave her easy access to the white stuff she'd started snorting, and, it is theorized, an income selling the stuff, as she had no visible means of support beyond her ex's child support) and the judge STILL awarded his ex full custody, apparently based on the theory that "children need their mother". Guy was even willing for his mom to raise his kid, if the judge wanted a woman for whatever reason. No go. Sick, sad case. (Privately, in our burg, we often wondered how this judge got away with some of his decisions. . .) Anyway, the guy apparently saved up his money, studied Spanish and disappeared with his daughter one day. I don't know of anyone who would've turned the guy in if they'd known where he was going.
That is totally different from hiding your kid at your mom's house, IMHO.