I am also a mom to 2 who does a lot of travel alone with two kids long distances (and sometimes the dog). If I'm going less than 8-10-12 hours, I generally leave at night around 6-7, drive until I'm tired, sleep, and finish in the am. I pre-plot possible locations to stop. I rarely do a campground for these types of trips, I usually use Cracker Barrels. I've had good success with feeling safe there and the kids LOVE getting up and grabbing breakfast before we get back on the road. If I'm going longer, I do opt for a campground, but tend to do the same driving arrangement. Drive the first night until 1-2 am, Cracker Barrel, drive daytime with my arrival time at the campground tied to check in time. It would really depend on just how long you want the trip to take. My kids 'haul' well, so they're pretty happy in the truck for hours on end.
I rarely unhook unless I absolutely have to (as others have said). I don't even put jacks down, just pull in, plug in electric and go. Now, if I'm noticeably un-level, in a campground for instance, I'd probably unhook or at least try to level out some.
If you're not a member of AAA or Good Sam or the like, I'd recommend joining - something specific to RVs. I speak firsthand how nice it is (with the kids especially) to have roadside assistance and someone to show up and not only take your truck but your trailer or vice versa. Worth it's weight in gold.
I don't worry much about safety, but I do try to think smart. My phone is ALWAYS charged when I'm alone (I leave it plugged in while in the truck) so that when we go back to the trailer to sleep (assuming we're at cracker barrel or a rest stop), I have enough charge for any emergencies. The kids (perhaps I'm a bit over protective) sleep in the front bedroom with me, rather than the garage (where I can't get to them with slides in, and there is a separate door to get in). I have pre-arranged times to communicate with my husband (or mom depending on the circumstances) along the route and those messages always give some idea of where we're at or where we're stopped. Generally I check in with him every 2 hours and then when we sleep (again assuming rest areas/cracker barrel, NOT campgrounds), he knows what time I'm expected to call or text in the morning. I've never had a situation that made me uncomfortable, but I like to think that being prepared is always worth it. My other two cents is a full toolkit. I've been known to learn the hard way (pre-kids) that my truck jack won't handle the trailer (get a trailer-aid and a solid jack), the wrench for the truck won't fit the trailer, 99% of the stuff these days is metric (so your standard tools on a 'leatherman' don't work lol), your spare might actually be flat unless you check it before you leave, detours stink.....
I always pay close attention to diesel stops (in some remote areas, diesel is hard to find, and some small gas stations canopies are too low for my 5th wheel). We often use the trailer bathroom over the rest stops (much cleaner with the kids, we use a scented trash bag for paper, unless I've put water in the tank). I run my fridge on the road, have a lot of bottle water on hand, etc.
It was mentioned about going around Chicago - I opt for those passings at night. The roads are far less congested, and usually it's easier to navigate. Only thing to keep an eye out for is summertime road construction that occurs overnight and causes backups.
I find this site and others very helpful in finding routes or stopping points. I've posted a few times asking for 'safe' places to stop, or routes to take that are RV friendly. Great bits of advice they've already given you!
I bet it will be a great experience for you and the kids! I wish I had the luxury of doing something similar!