Air Conditioner Can't Keep up
It does sound like the biggest opponent the AC is facing is the large picture window. I'm guessing it's just not a well insulated and/or not high-e glass and just letting too much heat in.

For starters, close the internal blinds. If that isn't enough, consider some exterior blinds. These aren't terribly expensive and shouldn't be something that the landlord would be against. 

There's different options for this. One is roll blinds:



This is likely the most practical commercial solution.

But you can get fancier as well with things such as shutters:



Possibly more expensive (more complicated to install) would be an awning:



Or a window trellis/arbor/pergola:



Before you invest in ANY of those, however, I'd do an experiment and cover the outside of the window for a few days with butcher paper or other large opaque material. 

If the AC can keep up just fine with that window covered, then one of the above options is likely the easiest way to solve this problem.

Other things to consider would be:


install ceiling fans. This does two things: one, creates a breeze to lower the perceived temperature and two, helps even out all the air circulation in the house. 
check that there are proper returns throughout the house. If there's only one main return, that can make it really hard for the hot air to get recirculated through the AC. Ceiling fans can help with that. 
make sure it's been checked out by an AC professional. It could be that it just needs recharging.