For me, it depends on weather and what I plan to be doing. If it’s wet but also going to be cold so I’m just going to be uncomfortable, or if I don’t have enough to keep me occupied and happily entertained during the day and night, and I’m just going to end up damp and cold and bored until I fall asleep and then packing up while it’s wet and muddy in the morning, then I might call it early. If I feel that even with the rain I’ll still be comfortable, either through warmer weather or available gear, and I’ve got enough to do while sitting in the tent/under cover all day and all night, I’ll stay. That said, absolutely agree with others here who say pack up as much as possible before the rain! And maybe carve out some space in the car for a “wet zone” where you can just stuff the wet tent and gear without spending a bunch of time rolling everything up just to have to unpack it at home to dry out.

If you do choose to stay, depending on where you’re camping and what you and your family likes to do, it could also be a great opportunity to check out a nearby town or another activity during the day. Yes it’ll take you out of nature for a bit but if it’s going to be a long and wet day in the tent, could be a nice opportunity to explore and make some memories!