I can understand wanting a nice home for your children to live in but, ultimately, I think YABU. Once you have left the home, you have no right to enter it again. Would you want your ex randomly letting themselves into your new place whenever they felt like it and rummaging around in your stuff?
Part of divorce is accepting you have absolutely zero control over how your children live when they are not in your care. If one's ex is a lazy, selfish, shit; this can be stressful, as you know the kids will suffer, but you can't do anything about it. Try to compartmentalise, so you don't spend every moment they're not with you worrying about them.
If the stuff bothers your ex, he is an adult and will find a way to resolve the issue himself - by either cleaning or hiring someone else to do. If you want to throw stuff out before you go, a skip can be expensive, but there are some great house clearance companies which will come, fill a truck and responsibly dispose of the contents. I had to sort a house out, had about 30 bin bags of rubbish, clothes, some furniture etc. I put all the stuff I wanted collected in one room, booked a local co with good reviews, they arrived on time, chucked everything in the truck and were gone with 20min.
I think you should focus on packing in boxes everything you/the children want to take to the new place. If you have time, you can make the house neat and tidy, but proper sorting takes months, especially if you have children who like to keep hold of things.