There are different meanings for the word “sex” especially for women. Sex can mean making passionate love where both of you have orgasms, or it can mean that you help him to have an orgasm without devoting too much energy and without having one yourself. So maybe you could have sex the first way once a week and sex the second way twice a week and that would be an acceptable compromise. I also wonder if he’s doing his share of the childcare, since it appears that you work a full-time job. Maybe if he did more, he’d be a little bit more tired, and would certainly understand how you felt when one of the kids was sick. I would also recommend that you work very hard at setting regular bedtimes for your children so that you can count on them being asleep by 8 and you both get some needed time off. I know that some working parents allow their children to stay up later so that they can spend more time with them, but I think that’s a mistake as it throws the family dynamics off. Children need to go to sleep early and you should make that a priority.