From the way you have described it, when you spend time with your kids, you are being a model for how they can spend time on their own. You have taught them how to draw, cut, build, play by the rules, be creative, read, etc. Perhaps your intentions were to have them go beyond a slugfest that erupts when they play by themselves, (I remember my brother and my interactions as kids!), but your have brought routine into their lives and it has enriched you and your kids.
Hubby works a lot and has homework because he is taking classes. He's tired and needs downtime. I've been there, too. I hope he finishes his classes soon so that he will have more free time in his life.
This weather has been horrible. I've got cabin fever in a bad way when I have time beyond my work to notice.
I think you both are right. the older boys should be able to "entertain" themselves when you need to step out of the house, and they should be doing something other than watching T.V.
Do an experiment. Next time when you leave, put out playdoh or art materials or a board game, and see if they watch T.V. or they use what you have put out, or if they do both simultaneously, or whether they just do something else. Try to cultivate their own ability to pick better choices. I've heard of jars with ideas of what to do when bored. The thing is that you haven't said the kids are bored. You've said you are bored. They may not reach out to the jar unless as a family you decide to restrict the T.V.
Sounds like the only time the kids get to watch T.V. or play video games is when you leave. Maybe that's their opportunity to use that equipment that has been provided to them. You could look at it that way.
When I have work to do, my DD typically starts out drawing or creating something, then role playing with the thing she created, reading a bit, interacts with the cat, and if I still have to work, then she will ask to watch a video. I guess she's earned it. She usually doesn't just watch, though. She usually draws or creates while it is playing. She's an only, and that does impact some of this issue.
Best wishes.