I live in a hot country so split ACs in every room. In fact our open plan area has four!
My experience is that they generally only work properly for the immediate area they’re actually in. Don’t expect satellite rooms to be cooled (without making the hall a fridge and still not great) or even a larger open plan to be uniform. The cool area doesn’t really spread out much unless you get a fan involved.
Best to pick a living space, eg an open plan living room or kitchen diner and have this as the cool space. Basically, you’ll end up with a lovely cool landing and an OK hallway. Probs not the priority!
Works surprisingly well with a curtain across and open door to outside if you want kids coming in and out. If that makes sense.
If sleeping is the issue then it’s tricker. Making sure the room, and everything in it, doesn’t heat up during the day helps. Doors, curtains, windows closed. Then open windows at night with a fan to get cool air in and give a breeze.