@amyers3 A lot of people on here saying "this is life." I don't think they understand you're trying to make full time work happen with only 25-30 hours a week slotted for your job.
I have an extremely flexible set of 3 jobs (all three involve writing, which is deadline driven, with flexible hours). I'm the carpool dad for my 4yo preschooler, who gets Pre-K from the hours of 9am to 3pm. I'm the sick day and snow day parent. I'm also the nanny parent when the sitter for our 1.5yo can't make it. If there are important family errands to make - groceries, banking, post office, etc., - I'm the one to do them.
Many weeks, I'm up till 1-3am trying to be a good parent/husband/employee. Just recently I told my wife we needed to make changes to our schedule or I would end up in a psych ward for a week recovering from a mental health breakdown. (To her credit, is really making strides to take on more of the mental and logistical burdens of the family - It's life's fault. Not her fault). Which is to say, I'm with you. It's unsustainable.
There are a couple of really interesting things I noticed in your schedule. The kids take baths at really interesting times. Is this because you only have one bathroom in the house? Is there not a school bus in the district that can pick your kids up? Any way you can deputize some of the bigger kids to watch the toddler during afternoon screen time so you can work on other things? I'm only asking because these are all things that stuck out as different than I have experienced in my frame of reference as a dad. I don't hear of too many kids taking showers at 2:00 in the afternoon, for example. I'm just curious now how much of your schedule is informed by your house, your hot water heater, or your number of bathrooms.