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There are two things that come to mind. The first is that your cat is chronically constipated. This can lead to a fecal impaction. Vomiting can accompany it.
I want you to try something very simple. Get some psillium from a health food store. You can usually find it in the herbs/spices/bulk food section. Psillium is a plant substance that is the main ingredient in Metamucil. But don't use Metamucil because it has other things in it too. Begin with ⅛ tsp. mixed in her wet food. See if this doesn't help soften the stool and allow her to have normal bowel movements, and stop the vomiting. If she is a large cat she might need ¼ tsp. Give it once daily. Psillium works by holding moisture. It softens stool and also helps with diarrhea. If she still has constipation she should probably be xrayed for an partial obstruction.
Secondly, if Pumpkin is vomiting without constipation, at her age, kidney disease should be ruled out. It can make her feel sick, vomit and lose her appetite.
Your recent move has no doubt stressed her. That makes everything worse.
One tip to get her to drink more water. Sometimes those fountain water dishes, where the water is moving, stimulates cats to drink more water.
You must realize that I am not doing a physical exam. I am responding to a small amount of information. There is no substitute to a physical exam by your own vet.
I hope that this has helped you Danielle. And I hope that Pumpkin will get better and enjoy her new home.
If you have any questions just respond to this email.
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