Hi - to echo what Josette and IHeartKing posted, part-time, 3 days a week teaching is a good work-life balance. It is important to establish your routine and what you do early on, though. If you are the only part-timer in the dept/faculty it is good to have clear groundrules and for them not to expect you to do the work of a full-time teacher, as you are not paid full-time! Equally those staff that come in and go, don't always give p-t staff a good name, well not where I work anyway.
Our dept/faculty has its weekly meeting on the day all p-t staff is in, which helps keep in the loop. I have to attend all parent evenings of the classes I teach, which is reasonable. I also share a form, which is better than being used for form cover all over the school!I have managed to share a classroom with another part-timer, which is working very well - a base for our resources and just a bit of movement when both in. Do ask for this if you can!
I do Inset days pro-rata, so 3 out of 5 if 0.6, and go in on days off if they are not on my working days. If school want you in above and beyond those days they can offer payment. Being proactive about when work as a p-t means you can book things in advance which helps!
Much depends on your subject and timetable as to how much work 3 days is I find - if end up with different ability groups in same year, or lots of different years it can feel like planning is the same as f-t. But if you get on well with your HOD or Head of Faculty you may be able to get a timetable of certain years, which reduces planning I have found - even if each year's timetable you change what years you teach. I teach yr 7-12 this year, but have managed to not have top and bottom sets in one year group, instead 2 bottom sets in yr 9 say, which helps!
All the best with your request. At my place of work, some people were turned down, but appealed to governers and succeeded.