I am right there with you! It is hard to get it all done and my kids also, hmm, how can I put it nicely – lack focus? I have ds6 and dd10.
I have cut way back on the activities that I want to do with them – they just are not interested in any of the “fun projects” I put together for us LOL – they just want to play. And I know that play is very important, probably the most important part of our day.
By afternoon I too am totally exhausted – I think I know just how you feel. Only I expect it is harder with 3 than 2 to wrangle.
A while ago I cut back our schedule dramatically. I had to do something because I was starting to dread turning to the studies in the morning. I spent some time deciding what was top priority for us. I wanted the kids to get plenty of sleep. I wanted to focus on reading with ds6 and math with dd10. To help me cope with our school time, I wanted them to stop asking to play on the computer or play video games during breaks from schooling. I also wanted to be done for the day at some point, if this makes any sense. I had to give up my dreams of notebooking pages and handicrafts (for now LOL!).
So our new schedule is : wake them up at 8:00, get done with studies by 1:00 (at that time I am done – put it all away! if I didn’t get all accomplished that I wished, I reflect on why? and try to do better tomorrow – but I need to be done at that time). Read aloud from a good book. Do math – both kids, reading (phonics) for ds6, grammar (Simply Grammar and Jr. An. Grammar combo) for dd10, Queen’s lang. lessons for both (this is very fast – but so good!). If that gets done, I am satisfied. In between these things is playing outside (nature study, I call it!) and snacks and breakfast and lunch. And if they want to look at library books or watch a video about something we are studying that is great but I don’t expect it. If everyone seems receptive we might read on our science topic or our history topic, depending on which thing I think needs attention (this is happening more and more often, I am pleased to say). No asking for electronic play before 1:00 (this has been very effective). And the habit we are working on is “doing as you are told” – sounds simple, right? :sigh:
These things are getting done. When I am satisfied with this for a month or so, then I will add to it. Actually I am already breaking this rule by trying to introduce composer study LOL with Prokofiev (Peter and the Wolf) but very gently.
One thing that I have done that has worked very well is to put my daughter in charge of art classes. She will put together a little something for us to do a couple of times a week, just on her own. It is usually just from her imagination and not related to our studies. She gets together the supplies and sets it all up, etc. I would probably not otherwise be organized enough to do any art lessons so this is great.
I also love the idea above of the wall of character traits mentioned above!
Since you have 3 kids in the mix, your days are likely a power of 10 more crazy than mine, and it may take proportionally longer to see an improvement in your schedule – I say make a long term plan to assess the effectiveness of whatever changes you make. Like stick with it for six weeks at least. I don’t often see overnight results in our homeschooling life – but we are not looking for a quick fix, we are looking into the future.