Is 实验动物中心 (experimental animal center) ambiguous in that it could mean either "experimenting on animals" or "experimentally creating animals"?
实验动物中心 sounds more like a place where they raise and offer animals for experiments, the keyword here is 动物.

If this is where animal experiments take place, then 动物实验中心 would be a better name, I think, because the keyword is 实验.

As for the meaning "experimentally creating animals" you mentioned, no, I will never think that way, nothing in this name suggests "creating".