The problem with Weston Park is that it is situated on the A5, with very little parking along it. I had a look at the Camper Jam website, and they show a Red Gate and a Blue Gate, but I don't know which of these would be used for entrance or exit or both.
There is a small lay-by on the A5 towards Red Gate (use Google Maps to find it), and there is another in Weston-Under-Lizard, which is nearer Blue Gate. There is a lay-by off Chester Road, which is a little West of Blue Gate.
An alternative is to pay for a day ticket to Weston Park itself, which includes parking.
Weston Park is not really geared up for "on foot" arrivals. It might be worth contacting the Camper Jam organisers for their advice too.
Pete