Hi, thanks again for all the feedback. I've been busy with the new semester starting (I'm a PhD student / teacher) since getting back from my trip. Here's an update (sorry for the length).

I did submit a payment to cover the vet bills for that dog despite feeling they were disproportionate to what happened. Along with it, I sent a friendly letter to the other people, apologizing, explaining the precautions I'm taking now, and introducing myself in attempt to alleviate their irrational fear of me (didn't put it like that). The management read that and seemed to change their attitude after that, though still no change in the lease situation. I also made them sign some stuff saying they would deliver the letter and that they acknowledge that the payment is not an indication of guilt/liability. After my last apartment (basic Brooklyn slumlord situation) I learned a few things about creating legally admissible documents. I think the way I handled it made them decide to check themselves in how aggressively they were dealing with us. But like I said, nothing has changed with the lease.

My intentions for the next move are to contact the board of directors, and also try to get my wife, instead of her dad, to start sending the rent checks. This is all very difficult since I am not the main person involved here. My wife easily becomes overwhelmed by stacks of opaque paperwork, and my father-in-law easily gives up on anything that's not watching TV while eating ice cream. When I bring it up with him, he always says how the managements' main strategy is to intimidate people ... then he doesn't say much else: I take it their strategy is working on him.

@JG:
I'm curious about what your board's "documentation requirement" is. My wife got a list of documentation to submit, which she did comply with, only to receive another one which was harder to comply with. Some of the documentation on the second list, she did not have because she had already given it to them the first time. Also, they'd requested pay stubs, which she provided, only to be asked for tax documents which cost hundreds of dollars to order from the IRS.

I'm also confused about the income requirement. As I understand, one's rent is a function of their income here. I've been assuming that this is why we have been feeling pressure to leave; we don't make as much as most people they could probably rent to (at least right now - once I finish my PhD I will make a lot more). But my father-in-law is paying less than what I paid for my last apt in Brooklyn, which was half the size and infested with mice & roaches; basically anyone living in NYC could afford to live here. So, @JG (or others), what is the income requirement? But really before I delve into that we need to speak with the board, rather than the management. In my opinion it is obvious that the management is corrupt, I only hope the board has as much power over them as you all have advised.

I need to talk with my wife again about what I think we need to do. But ultimately she needs to be the one to do it (I think), since she's the one trying to get on the lease. And for that I need to wait until the time is right; our lives are hectic and those times are kind of rare for now. But the clock is ticking....