I'm not sure if you are asking or stating, since you have a question mark at the end. I very much doubt AA will pay for a hotel (they don't do that for IRROPS!) and I think you should prepare to pay for one night on your own. The most likely scenario is that AA will rebook you to AA, not to UA.

That said, 1:56 is tough to call. You might make it, but as was said upstream, there are plenty of other intl arrivals at that time. For TATL to US connections at airports like that, I generally like a three hour window. Sometimes excessive (in which case I have a shower), but past experience tells me that this is the comfort zone.