First, it's important to remember that stuff happens. No matter how well you plan or prepare, unexpected problems can occur ranging from minor (nail in tire) to major (catastrophic engine failure). But you already know that, and you are intelligently planning to take reasonable steps to plan for and/or avoid foreseeable problems. With that in mind, I'll describe what I do before such trips, and you can decide for yourself which measures make sense for your situation.
This goes without saying, but I didn't want it to go without saying: prioritize safety first. As a practical matter this means, for example, that if you have to choose between fixing the 8-track player or replacing the wiper blades, you should choose the wiper blades. So the basic things that anyone should check would include:
- tires and tire pressure
- windscreen wipers and washer fluid
- all lights and horn
- brakes (check pads, rotors, fluid)
- wheels and lug nuts
- exhaust (mostly check for leaks/holes)
- safety belts/harnesses/car seats and mounting
- seat controls (do all driver seat controls work?)
- mirrors (all intact and adjustments working)
- driver (be well rested, attentive and careful)
Check major systems
You mention that the vehicle has been driven hard, but really the more important consideration is how it has been maintained. Has it always gotten oil changes on time and are tire pressures monitored and adjusted? Are the wiper blades new-ish or torn up and crumbling? I know you're just borrowing the vehicle and not buying it, but it may be helpful to imagine you're buying it. Evaluate the vehicle dispassionately, and carefully. To that end, after the safety items already listed, I'd look at and/or inquire about:
- oil level and condition
- transmission fluid level and condition
- engine belt condition and adjustment
- suspension and bodywork condition
- shock absorbers (dampers) condition
- engine coolant level and condition
- radiator and hose condition
- power steering fluid
- battery condition
- all driver controls (steering, pedals, emergency brake)
- all doors and locks
- hood and trunk/hatch latches and releases
If you had to make a sudden stop, is that heavy bag secure or is it in danger of flying forward and injuring someone? In a passenger car, I try to put nearly everything in the trunk for two reasons -- first for safety and secondly so that if I stop at a rest stop, there isn't anything obviously attractive to steal.
Pilots typically file a flight plan, and so should you. It doesn't have to be big and formal, but somebody you know and trust should have at least the outline of your intended trip. I usually email a friend or relative and let 'em know where I'm going, how and when. That way, if anything bad happened, at least they'd have some idea of where to look for me. (Pro tip: make sure it's somebody who would both know and care if you went missing!)
Make sure you also build in time for adequate rest. Your trip will be more enjoyable and you'll be a safer driver.
Sure it's "just US and Canada" but it's probably worthwhile making sure that you make sure you have all necessary and useful documents. For example, if it's a borrowed vehicle and you got stopped at a random traffic stop, do you have sufficient documentation to indicate that you have insurance? That you didn't steal the vehicle you're driving? That you're not kidnapping those infants? That all might sound like a joke, but things can get serious if you even unknowingly break a law, such as this young woman who was detained by US immigration authorities for two weeks for inadvertently crossing the border from Canada into the US while jogging on the beach.
Personally, I hate a messy car. Before a long trip, when, especially with kids, things can get messy, I usually try to wash the car and clean the interior. That has more to do with my preferences than with safety or reliability, but I also usually also do stuff like replacing (or at least checking) the interior air filter and making sure the flashlight in the glove compartment has fresh batteries. I also usually take some minimum complement of tools, but that's only useful if you'd also be prepared to use them.