Looking at the pics, the tree is definitely in the public R/W, however, because there is no sidewalk, you may be able to convince the city to allow you to remove it.
However, the other issue is that the trailer in the pic is also extending into the R/W, which in my city would result in a code violation. Drawing attention to it may result in the tree remaining and the trailer being removed.
The other option, as some have suggested, is to remove it yourself (or hire someone) on a weekend. But I wouldn't do that unless you talk to your surrounding neighbors and get their tacit approval; never know if there is a tree-hugger living there that would turn you in, resulting in a large fine.
