Hi Twilight Joy! Wow, 18 weeks, I can't believe it has been that long since we both got BFPs!
First, how valuable/replaceable are you? This will help determine how "demanding" you can be. Basically, if they truly value you, you can frame it as, "This is the schedule that will allow me to balance my work and family responsibilities."
1. Definitely spell it out for yourself in writing. Write down your argument and practice it multiple times. You have to demonstrate how (1) you will be able to fulfill all of your responsibilities and (2) the company will get all of its needs met. Only you know all of these details. It probably makes sense to suggest a regular schedule when you are part time, so that they know when they can rely on your rapid response, and when you are doing other things (unless you are prepared to respond to emails all the time, for example, which might be better, or not, depending on your work). Have you thought about the implications for your benefits, etc? Important to think through every detail.
2. Go to your boss and talk, don't do it in a letter or email. There is much more room for negotiation in a conversation. But be firm in what you want, present it in a way that looks beneficial to everyone and is nonantagonistic.
3. Once you have verbal agreement, put it in writing and have your supervisor sign off.
I decided about 3 months ago that I wanted to work 20 hours, and that I deserved higher pay. I didn't think it was reasonable to go in and ask for both, and decided I was going to instead quit and try to figure out another way to make the $$ I needed every month. I practiced my quitting speech several times, and remember telling myself not to pause so that he couldn't interrupt (because I knew he would try to convince me to stay). I had thought through exactly what it would take for me to be happy (20 hrs and more pay/hr), and so I was able to negotiate exactly what I wanted, on the spot. He threw out the number 30 hours a week, and I said, no, it would have to be 20, but that even then I wasn't paid at a fair rate. I could not believe how effective I had been when I got out of that meeting, and it was because I was not happy, knew exactly what it would take to make me happy, and was willing to risk losing the job in order to get it (not sure if same is true for you). This tactic, while I would not recommend it in most cases, ended up being very effective! I suddenly had all of the bargaining power.