I would ask and get some clarification on work hours first. Just ask them to be clear with you on why they want you for the position at part time. I'm sure they know you are coming from a full time position (or do they?). Their answer on the hours will let you know before hand if their is wiggle room, because you will either need compensation to make up the difference of what you are making now (with less hours) or more hours. If the hours are not guaranteed, I'd focus on compensation.
Let them bring up the subject and make their offer first. You never know, but they may come in with a salary higher than what you are making now, but with part time. Not likely, but you will most likely lose if you put out your compensation expectations first. Think if they had planned to offer you $70k, and you come in at "needing" $65k first. Then they may say "sure, $65k is fine," and you just lost out on a possible $5k. Keep emotions out of it. You can always counteroffer, but that doesn't mean they will accept. All you can do is try. Whatever you do, if they go the direction of starting you out at a certain salary, and then raising you up later, be sure that you get it in writing on exactly what time frame that will be. If they are not willing to do this, I'd walk. If they are, expect them to have some stipulations, such as whether or not your performance meets their expectations, your attendance is good within that amount of time, etc.
