looks like the original mug designers files a dmca take down notice which is a process that can and has been used legitimately and illegitimately.
If you feel you have not violated any copyright, you can file a dmca counterclaim which entitles those who originally complained, your contact information in order to pursue legal action if they wish. By filing a counter claim amazon can then reactivate your ad (assuming there are no additional measures/hoops you need to jump that amazon has self imposed.
1) Did I violate any copyrights?
I dont think so. Its certainly a knock off, and its an obvious copy of the original idea, but in US ideas are not protected by copyright. One would have to ask, what copyright protections can be made for the original design. The shape of the mug is not protected or at all original. The font and collection of jokes can be, but you did not copy that. The design of the mug with a large "Emergency Dad Joke" in the middle with joke blurbs floating around it can be and that is where some may find that you have to a degree copied, but is that design idea original enough to prevent similar mugs with completely different content from taking form?? I would think no.
Usually a threat of a lawsuit and its costs are enough to scare competition away from the marketplace.
I recently received a "have a nice day" mug, and just now googled and enjoyed the variations I saw. I believe its a similar scenario.