Hi, Raoulpetite,
I'm sorry things are still tough for you, but I'm glad they are getting a little better, especially compared to last year (is my impression from your earlier posts). We haven't homeschooled yet but might in the future--that is one thing that puts me off, is that my DD9 probably wouldn't listen to me very well and it would probably be a continuous power struggle. However, over here (in the U.S.) many cities have homeschool groups of parents who work together to trade advice on curricula and other things and some are even organized enough to take turns organizing classes or workshops in their area of expertise (at an appropriate level for the kids, of course). Is there anything like that there that you might be able to join to help ease the burden just a little? Also I understand that your DW is stressed, so maybe hiring a babysitter for a day a week, or an afternoon every now and then, might help her get some time to unwind and face the next day with renewed energy.
I'm sorry I don't have anything useful to say about the behavior issues...I have used timeouts with our DD to good effect, but every kid is different. She does best with clear rules and gentle reminders necessary, followed quickly by predictable consequences if she breaks the rules (consequences such as losing video game time, dessert, etc.). Also with our DD we tried to give as many choices as possible--do you want to work on math now, or go for a walk first? and that seemed to help her. I know there are a number of books that have been discussed here that seem to help people, although I don't have personal experience using them; perhaps some of those would help.
Sorry I don't have better advice, but I wish you and your family all the best! Good luck!
