You could set up a little contract to check off before you submit images? Saying that the person has the rights to the image their submitting, and they give up the right to have it taken off the site without.. good cause?

Maybe something of that sort? I don't think the legality of it would be too big of an issue, but on the subject of the owner of the actual animal wanting the image taken down, I believe they have no legal right to say so. The image is not theirs, just the subject involved. I am pretty sure there is a law protecting photographers who take images from people changing their minds later and throwing a fit about said images. (I do photography, but haven't gotten into the nitty gritty of the rules.)