If you think there might be important changes in the editing of the first part, I would work on that first, before writing the second part. Otherwise, the second part could prove to be all wrong later. Just don't let yourself get caught up in continuous editing of the first part so much that you never get around to the second part.
I speak from current experience, here.
I wrote the first 50k words of my WIP and then didn't touch it for a year. When I got back to it, fairly recently, I found myself stuck in a loop of tweaking with no clear idea how to move on. For future reference, I found my way out by sending some of it to a couple of fabulous people whose commentary showed me the path. But if I had tried to write the second part before that, it would have turned out useless, as the recommended editing led to a number of important changes in the first part.
On the other hand, if you can see your way clear to the end right now, and don't think you'll be changing anything that will affect the second part in a major way, then get it out while you still can!