Hi Jan, YouR out 12 1/2 hours a day with mixed sleep, you come home and help with your child, and do studying, and your wife can think why she is not getting any sex during the week, even when I was working and doing very long hours, the last thing my wife would be thinking was sex me up, to bussy getting thing ready for me the next day, come saturday we relax put our feet up less stress and away we go ready for sex.
I think somebodys with is a bit paranoid and clingy, its about time she grew up, shes acting like a teenager, if she wants to know what your doing tell here to follow you to work.
Good Luck
The answer for damn near everything you mention is **'s. .......... or Viagra.
Maybe try courting your wife a little during the week, so that even if there's no sex involved, she sees that you're still attached and attracted to her. Maybe get her flowers, or write her love notes. If it won't interfere with your workdays, send her romantic texts during the day. If she's really paranoid about cheating, you could offer to send her a picture of what you're doing right then whenever she asks (assuming you have phones that can do that). It might be too impractical, but it's a thought.