It depends if there are any laws that require a landlord to allow you to be able to get direct access from a ISP. This is why apartments are forced to allow satellite dishes. You would think you could get DSL in any case, unless the apartments have decided to force their phone service on you too.
You should with care be able to use both connections at the same time. You could run your ones that require high speed over the 4g and the ones you can tolerate some slowness over the apartment. This is done with the ROUTE command. There is software from connectify that will help also or you can get a dual wan router that support 4g modem. Many asus or tplink have the option just be sure your phone is supported.
If you look at apartment locator software one of the big requirements is to be able to search for internet type. Many people will choose a place to live based on the type of internet they can get so your apartment needs to get their act together and start allowing private internet connections. If they want to offer free internet that is one thing but to prevent you from putting in your own connection is quite another.
They are lucky I don't live there, I would give notice and then the full week before I was going to move out their internet would "mysteriously" be completely unusable.