South Dakota Gov. Kristi Noem’s chances of becoming Donald Trump’s running mate are as dead as the dog she executed in a gravel pit — according to the president’s own allies. The Republican governor revealed that she had gunned down her family’s 14-month-old puppy Cricket for misbehaving and then dragged a smelly goat into the gravel pit to meet the same fate, saying in her forthcoming political memoir that the killings showed her willingness to take on “difficult, messy and ugly” tasks, but sources around Trump were just as horrified as everyone else, reported The Daily Beast. “Everyone arou…