first: spay her. this will PROBABLY help to cut down on aggression issues with the new cat.
second: go younger. older cats seem to accept younger/smaller cats better.
third: i would wait until after the move, just because bringing home a new cat prior to a move is a LOT of change for that cat to handle, and you’ll want introductions to be slow (at least a couple weeks of no-contact aside from sniffing under a shut door).
in the interim, research methods of bringing a second cat into the home. there’s a lot of info out there, and doing it right can mean the difference between getting along and wanting to kill each other.
Dogs can get digestive upset from abrupt change in food, particularly kibble. The main question is whether that’s what did it or whether it’s a coincidence. It is likely that’s what did it, though. That’s why gradual change is recommended.
Another thing to consider whether your dog is dehydrated at this point, or in pain, or in more serious distress than the diarrhea itself. Still acting normally? Playful? No lethargy? I any additional signs of concern, I’d contact a vet.
If not, I’d let the system rest for a day with providing just water or potentially home made broth or bone broth. Then the question is whether bland diet (such as boiled chicken with rice or white potato) is a better idea or whether it’s best to return to the original kibble, let things settle down and if you still want to change do it very gradually.