The arrangement is not new--we have had it this way since March. The way it works is one week he has them three nights (Sun, Mon, Tues) and the next week four (Sat, Sun, Mon, Tues). So, it does come out even.
Someone mentioned this not being a common arrangement. What is more commonly done?
So basically he has then Sunday, Monday, Tuesday nights, you have them Wednesday, Thursday Friday nights, and you trade off Saturdays? I've heard of this before, and it is okay if you don't mind not getting a full weekend ever and it works for you.
Are your kids in school? The issue may have something to do with the mid week transition, but with that schedule it would be hard to change it. If they are in school, definitely try to have one parent drop them off and the other pick them up so there are no parent-to-parent exchanges, which I think is much easier on the kids.
Other common 50/5 schedules are 2/2/3, where one parent has them Monday/Tuesday, next has them Wednesday/Thursday, next has Friday/Saturday/Sunday, and then next week you switch. Of course, then you don't have them the same days each week, which can be make scheduling tough and this wouldn't really solve your mid week transition issue.
2/2/5 keeps the same days and alternatives weekends (parent 1 has Monday/Tuesday every week, parent 2 has Wednesday/Thursday every week, then switch off Friday/Saturday/Sunday) Again, though, the midweek transition.
Of course, there is week on week off, which solves the transition issue but is a long time to be away from the other parent and your kids seem young for that.
Actually what sounds toughest to me is not having an entire weekend with them (it sounds like only every-other Saturday?). Activities like camping or a road trip to Grandma's house come to mind--not anything remarkable, just the ability to have a couple days to decompress and experience the fun times with kids instead of just the school day grind.
To help the kids through that kind of schedule, I think it is extremely important to structure both households the same. There should be as identical as possible schedules (get up, go to bed, possibly even get ready for bed routines/expectations), rules, etc. Obviously that requires cooperation between you and your ex, both to tell you how things go in each home, and for you two to agree on what the schedules and rules should be for the children (co-parenting) instead of you each forging your own course (parallel parenting). Hopefully child rearing decisions are not something you clashed about previously! If you and your ex are on OK with it (and if it seems like it would work for your kids, that it doesn't get them too worked up) it might be nice for the kids to call the other parent an hour or so before bed, so there can be some consistency there too--that they can say the same silly before-bed limerick and their "I love you"s to each parent every day. Nothing long and drawn out, just a quick good night. If all else fails, ask them how they want to do something and follow their lead.
I would make their time with you also as predictable as possible. That might mean that every Wednesday night you make homemade pizza (or something else you all enjoy that is fun to work on). On one hand it seems boring, but I think to young children it's more secure and comfortable than boring.
Kids are excellent at sensing what's going on around them with their parents. You know how when they fall and scratch their knee, they look at you immediately to see if they're OK or should cry? That's how they operate with everything they're not sure about. So if you can appear strong and confident about them being with you, they will pick up on that. If you seem frazzled and unprepared for parenting time, they'll probably pick up on that too and feel more stressed themselves. Maybe you can make your preparations into a game, like "I don't have the things we need to make dinner tonight, let's see who can think of the silliest dinner we could make while we drive to the store!" to keep all of you low-stress.
I believe in some states 50-50 schedules are the default. Others assume one parent to be the primary parent and the other gets only every-other weekend and 2 weeks in summer by default. I actually think schedules where kids have 2-4 days with each parent are quite nice, so they get to see both parents a lot but never have to go without seeing a parent for very long. But that's in theory, so if kids can't cope with all the back-and-forth, then other solutions might be explored. We have DSD for 3 months of summer and then she's with her mom for 9 months of school. DSD often talks about how she wishes she could not have to go so long without seeing one or the other parent. There's no winning; no matter how you slice it, kids are losing out on seeing one of their parents every day when their parents don't live together.
I don't have any advice on getting yourself switched to parenting time. For me, since we're facing such a long stretch of time with DSD, the first couple days are usually spent doing unsustainably fun things, just to celebrate the new time together and (dare I say) break the ice. We have time to make the transition together, but if there would be only 3 days before separating again, it can't work for you how it does for me. Maybe it will get easier for you when you start seeing it be easier for the kids--if you think that might be true, maybe you could throw yourself into helping them through it and wait for it to get easier for you too?