OK...
Weather - East coast is good, drier than west coast. If you are going before the school holidays (ie before campsites are booked solid) and can be flexible about dates, you could wait until close to the time and book when the weather looks OK. If that's not possible, research your area and find some indoor things to do when it's wet, look for non-touristy things like soft play, as well as touristy things.
Wrecking the tent - I think tents are actually quite difficult to wreck. Their very flimsyness is actually an advantage as they tend to give rather than break. Unless your toddler has sharp knives to play with, in which case the tent is probably the least of your worries
. Speaking of sharp knives, gas etc, we tend to lock them in the car boot while we are in the tent and leave them in the tent if we go out in the car.
Bolting - I've never really had a bolter so I haven't much advice. A larger site might be better as it's quite easy to escape from a small field and a toddler would have to get a long way to escape from a big site. Look at hazards as well, a field within toddling distance of a river, for example, might not be a good idea either.
Disturbing other campers - well he might, a bit, but that's just one of the hazards of camping. The odd wake-up and quick cry wouldn't bother me if I was camped next to you but an all night screamfest probably would. If he already sleeps well, chances are he will sleep well when camping, especially if he has done lots during the day and provided he is warm enough - lots of layers, socks and blankets underneath as well as on top if it is cold.
I'm guessing he is still in nappies. If he isn't, consider putting him back in them at night as a wet bed when camping would be a nightmare to sort out.
I'm sure it will be fine and if it isn't, it will be a tale to tell when he's older! Have a lovely holiday.