Ohio's breastfeeding law covers "privately property" such as Magic Mountain, in that it is a place of public accomadation. It does not matter that it is a "family establishment" either.
Another mother, a few years ago, was given issues about nursing her child in a fitness club. She filed a complaint with the Ohio Civil Rights Commission. Not much came of it, because she and the company settled the issue before it got very far, but the Commissions rulings to date had been in Mother's favor.