Oh Boy - What a can of worms. I am so very sorry for you and the situation you are dealing with. You have my compassion and I wish you strength.
As for custody - go for 50/50. Especially if she is "exhausted for having them 24 hours a day". 50/50 is really the best method to cope and keep it equitable. One week hers and the next week is yours.
As far as the scheduling goes, yeah, that is what I have to do. We just have to deal with scheduling appointments, scouts, soccer, etc... on the days they fall on. If you each take a week, then it is more manageable.
Each of you has the responsibility for attending or not the event for your week. For example, if your week is scouting and it is too much, just cancel it for your week. Don't ask the W or consult with her, just cancel it. She has the right to do that as well when it comes to her week.
My suggestion is that you BOTH fill out the calendar, don't just let her do it as it will only make you upset when you start to resent being overscheduled.
Your post felt passive and I felt like you gave your W too much of your power (time, energy). Don't let her do that to you. You schedule what you need and anything that is too much just say "Can't do it". You do not have to defend your choices to her anymore.