“In the state of Ohio, is a parent allowed to cross state lines with a child during guideline visitation?”

Generally speaking, so long as there is nothing in the court order disallowing it, and so long as the parent returns the child on time, there is nothing wrong with a parent taking their own child across a state line.

However, that said, every state has its own little idiosyncrasies, so you would be best advised to check with an Ohio family law attorney.