Once, I made up a big chore chart for the entire house, put everything and everyone on it, including my husband by asking him which weekly chores he would be the most likely to complete without having to be reminded by me, the CEO of the household. I divided the chores up equally between all. When he is in town, he does his part.
Some men really do need a list. They just don't walk around the house looking at all the work that needs to be done, unless they were raised by a great mom who taught them to pick up after themselves. You could start a chore chart, as that would even help your 12 yr. old SD. You could start a Honey Do Jar....I write 1 item per piece of paper, fold it 1/4's, put it in the jar and when he has some time on the weekend, he'll pull one out and work on it.
But my first husband was a complete slob and we clearly had different tolerance levels for filth and that ended in divorce. There was no willingness with him to compromise and help. I was not about to be his mother the rest of his life.
Also with some men, once you 'do' something once, it will always be yours to do again. So choose wisely what household task you will take on.
You must learn to speak up constructively. Don't nag and whine. Write up a daily list. Show it to him by txting, email, leave it on the kitchen table where he can 'add' what he thinks need to be done as well. I always tell my husband my list of to-do's for the day, and over time he knows my workload and will often say, "Honey, I can tell you will be having a very busy day, it doesn't look like there will be time to make dinner, so let's go out." I would much rather he help cook a little. But I hope you see the point, include him in all that you're up to, put it out there so he can't claim he doesn't know how busy you are.
EDIT - I did what Victoria did with her husband. I went on strike, with Hubby #1. She was smart and took a week off. I just went on strike to see how long it would take him to notice. After he had used up EVERY single dish/pot in the kitchen and ALL paper products did he finally go in to the kitchen and do the dishes. I had a 4-5 month old at the time and was working full time. I agree with Victoria it was gross. But that approach never did much for that relationship. I still recommend a confident approach, with a smile and an all-inclusive, were in this together approach.