This has been on my mind recently as I have this year gone part-time in a new school for my return from maternity leave. I’m fortunate that I am in a school where there is a culture of supporting part-time staff, and one part-timer on SLT.
You need to start managing expectations, because no-one else will do it for you. No work email on personal devices like phone or iPad. As suggested by a previous poster, PC only and make it a little bit more of an effort to log in - don’t have your password saved, for example, so you can’t do it mindlessly. Make sure that your line manager knows that if they need to contact you urgently on your day off they’ll have to text or phone you because as far as they're concerned, you are not available via email - we’re talking once in a blue moon events like notice of an Ofsted, emergency closure of school due to gas leak, etc. Make plans with your DC on your days off so that you are out and about and not tempted to check email during a quiet moment at home while they nap!
You need to train the people emailing you that you are part time. If you absolutely have to reply, send a polite line: ‘Thanks for this, Bob. I’ll look into it when I’m back in on Thursday.’
If it’s more stressful to ignore the emails, then allocate a specific time to deal with them, do the necessary work, compose the email response, and DO NOT PRESS SEND. Save it in your drafts and spend sixty seconds in the morning when you’re back in pressing send on the emails that you’ve stacked up. It will take a while but gradually you will train your colleagues to think twice before emailing you on your days off and they will learn that you need reasonable notice for tasks.
If your job share isn’t pulling her weight then you need to start compiling a log. After any conversation where you agree on divisions of tasks etc, send a quick email to follow up: ‘Thanks for your time, Jane. As discussed, I’ll do abc and you’ll do xyz.’ You need a paper trail of your agreed division of work, but if this doesn’t help then start to copy in your line manager.
Finally, I find that it’s harder to switch off if I’m trying to hold a lot of things in my head. Get yourself a notepad or a task-management app and do a 'brain dump' periodically (before bed, when inspiration strikes in the supermarket) so that you don't fret about forgetting anything.
Good luck 