HUD and the Civil Rights commission do not initiate an investigation until you file your complaint. There is a statute of limitations that applies, and that does not stop running until you file your complaint. You are correct that a threat to evict you because you have an assistance animal (the correct legal term under laws requiring accommodation of disabilities in housing) could be considered retaliation, provided it is considered reasonably severe enough to dissuade you from asserting your rights under the law AND your means of asserting your rights were reasonable. From a cursory review, I would question the reasonableness of your own actions. I do think it would be considered quite more than coincidental that both you and your wife had such a quick, immediate need for assistance animals in the very same week, right after moving in. May I assume you already had these cats? It seems illogical, and yes, disingenuous, that you would suddenly develop the need for an emotional support cat if you were not already attached to the animal, in which case your claim of an actual medical need could be considered suspect.
Regarding moving out with no notice, everyone on the forum who has responded would seem to have the same opinion and I have nothing else to add.