I think that's sad. :( You're a single mom and he can't know his kids on a hour a day, plus dinner and Tv.
Not to be preachy, but since you asked, I would suggest focusing on your family connecting with each other rather than a responsibility chart on who does what when. I would suggest a date night every other week and a family day every single week, to start. Plan a fun outing or some games, I don't know what your family is interested in but something that will help you guys learn each other and have fun together. Perhaps since there's such a big age difference with the kids, you guys could take turns picking days where you choose to do something that person is interested in (mom's choice, dad's choice, son's choice, daughter's choice). Play some talking games: stuff that gets you talking is a simple way to get to know someone, and can be done at dinner time (what was your favorite part of the day, your least favorite part, if you had, found, or lost a million dollars, what would you do with it, if you could be anything in the world what would you be and why, etc), or we have this little dice game where it has words on the sides and you toss the dice and come up with a little story using those words, all kinds of little things like that....it lets the kids have a voice and you get to see how their minds work and what's important to them, but you also get to share yourself with them instead of just constantly running on the hamster wheel everyday.
We have a date night every month (sometimes twice, but always once), a family day every week, and over the course of the month we also switch kids and I do something special on a "mom date" with each boy separately (husband watches one while I have the other), and Jeremy has a special "dad date" with each boy separately. (Example: last week--family day was sharing icecream out (I shared with the older, Jer shared with the younger), then we went on a dolphin cruise, climbed a lighthouse, and ate out. Jer had a "dad date" with the 18 month old because he had to drive him 2 hours to a pediatric ENT to be checked, but then they stopped at a playground and played, they ate lunch out and he ate at the table instead of a high chair and practiced using a plastic fork, and they walked around and collected rocks and pinecones. He was so proud to bring me his bucket of rocks they found when they got back. Simple stuff. Their first "road trip". While they were gone, I took the eldest (4) out of daycare early to go to a car show and see all the cool old cars, and he got to sit in a few. We went to the river and practiced skipping stones and talked, and fished a little bit before he had to go to karate class. We share babysitting time with a friend from my mops club and we went week before last to a habachi and then saw the community theater's version of Chicago. This is not to say we're perfect. I get annoyed now and then when he gets into this little phase of working too much. We both have a tendency to be workaholics, and we just have to keep it in check. Work is important; we wouldn't be able to pay the bills or live in our house or whatever, but it cannot be ALL the time.
If you can get your family priorities in line, perhaps the other stuff will just fall into place, or at least fit better. As for dividing stuff up: during the week my husband works a lot so I do the housework before he gets home so that we can hang out when he is home. He gets home and hangs out with the boys until dinner time, then I bathe them and he reads the story (but we read the bedtime story on the couch and I cuddle in and listen too even though there's other stuff to do), then we review the day, say prayers, and then if he's really tired I put them to bed (seems I always brush teeth unless I'm sick) but if I'm really tired, he'll put them to bed. Whoever changes the diaper is whoever is not doing anything or notices first. If I'm cooking obviously he's changing the diaper. Or whatever. On weekends, I try to have everything done already because I want to PLAY, but if not he'll either take the boys out so I can get stuff done or he'll help me, depending on how much or what needs to get done. It's teamwork. But I think you have to build the team before you can practice teamwork.