IMHO - I wouldn't touch it. It's easier to mess with the car stuff than the house stuff. Maybe a refi is different. I haven't been through one yet. How much lower will your new car payment be vs the savings on your house? How long the lower apr rate will be offered. Can your Fico score take a new HP since it would be a second HP within the year.
I think it depends on how much money you would save? If it's a significant amount I don't think "one" HP would be detrimental.