Many times I’ve talked with renters concerning this very thing. Why won’t my landlord let me fix something at my cost? The answer is two fold:
ONE: The landlord could be held liable if something were to happen during the repair. The risk is not worth it to the landlord. This is a big reason why landlords refuse to allow anyone to work on their properties without being licensed and insured, or someone they have a relationship with that they feel won’t bring a frivolous lawsuit.
TWO: The property belongs to the landlord or his client. You may be able to have it repaired for a lessor amount, but the only way for the landlord to ensure that similar quality is to have it done by his own people.
The best way to get around this is to “Ask for forgiveness not permission.” Meaning that next time you may want to have your unlce come over and fix it, if the landlord finds out you had repaired something without his permission he may be mad for a bit, but it probably won’t get you evicted.

Do you have renters insurance? If you do you should consider filing a claim with your renters policy. Theres no reason you should foot the bill if you are insured. Also, the insurance company may be able to say that its not your responsibility. Then, it will be up to the landlord to have the shower dorr fixed at their expense. Even if you don’t have renters insurance, I’m certain the landlord has an insurance policy that will cover this kind of thing.