Is it easy to rent a car in Copenhagen to drive to areas around Agerskov
Yes, easy slow driving. More traffic around Copenhagen.
Consider also airports Billund and Hamburg (Germany).
It's even easier to take the train to e.g. Kolding and rent the car there. Saves you a long (and boring) drive, and means you don't have to deal with the traffic around Copenhagen.
Also, it's easier to follow what you plan to do if you continue in your existing thread.