I take my four DC camping as much as possible. Pre-covid it was a weekend once or twice a month, for the entire season with two or three 7-10 day trips.
We invested in an air tent which is so easy to put up. We have the berghaus air tent and I highly recommend it!
When the children were much smaller, I would rent a tent through eurocamp or similar. It really does make life simpler, especially if you are just starting out.
On the trips when DH wasn't with us, I kept things as simple as possible. Nice walk, swimming pool, simple food (I planned all of this ahead of time) bbq in the evening. I would go to bed with the kids and wake up with them. Your DC are old enough to help out with the food prep and the chores.
The drive would depend on the destination and how much it appealed.
Sometimes we go to a campsite that is 15k from our home but we would also drive 7 hours to camp near a theme park that we all loved!
Good luck... it will be great fun!