I am trying to find a device that I can plug into the wall, then plug another device into that will offer overcurrent protection. Basically, a circuit breaker that will trip before the actual circuit breaker will trip. My reasoning for this is that I am staying in a cabin that has 14 outlets wired into it (think of a shed with outlets), a ceiling fan, and lights all on one circuit breaker. I do not have access to the breaker box and do not want to trip the breaker if I plug in a window AC unit. If I tripped the breaker it would disrupt my cabinmates, and we would have to get maintenance to come to unlock and reset the breaker (1-2 days for that). The device I have in mind would basically stop my AC unit from tripping the breaker and would tell me that it is too much.
What you need is a plug-in electric meter. It's called a Kill-a-Watt and it costs $20-30. Every time you turn something on, go check the Kill-a-Watt and see what you're pulling. It offers several figures, the one you want is amps.
I gather you don't have a foggy clue how much power various devices draw. You'll get edumacated right quick with this!
As long as the lights are LED, they and the fan will surely draw less than 1 amp together. If they are not LED, make them LED.
Also, if you are paying for this facility, 2 days to reset a breaker is a violation of tenant occupancy laws, and they are violating state law by renting a unit with that problem. Contact the local government and report a fair-housing violation. Such a problem is acceptable (e.g. In a hotel room) when there is competent on-site maintenance capable of dealing with the problem in a sub-1-hour time frame.
Now if you are the provider and you are installing this, that's a horse of a different color. I would expect any day now, the inspector to show up, spend the whole day, and have to call down to City Hall for more red tags. However...
You should have a service panel in each unit, and the main breaker in that service panel must be a shunt trip type. These allow "remote" trip of the breaker, or to be more precise, allow electronics to artificially induce a trip. You could use a GFCI breaker and have your electronics induce a ground fault, but a shunt trip will be far more intuitive for users, since it looks like an overload trip not a GFCI trip.
Then, you'll need to build an Arduino style gadget that sits inside the local breaker panel. It has a current transformer (CT) on the incoming power so it knows how much power is being drawn. It has one job: activate the shunt trip before the remote (inaccessible) breaker trips. So it will need to know the trip curve of that breaker.
This won't protect from all situations like a dead short, where it's anyone's guess which breaker will trip first. But in simple "too much stuff plugged in" overloads, it will do the trick.
It would also help to have an ammeter on the service panel, so occupants can see how close they're gettng to trouble.
Also... Don't punish tenants for not knowing what appliances draw... because you don't know yourself. Most people don't. You know how to find out, but you have to look, right?