Have you ever asked him to pack the kids lunches, like on his two weekdays off? If not, I'd ask that he take that over on his days off. Also, why do you all the cooking? If he claims not to know how, teach him. You could, together, do a big cooking day where you two make big batches of food to portion and freeze so that most days, you won't have to cook from scratch. Does he do the dishes or laundry? Does he have any guy friends or is close to siblings/parents, or not? What brings him joy? I'm just trying to get a bigger picture of the situation. Does he seem to enjoy the children, or does he just see them as nuisances, etc.?
I'd probably ask him, to get some idea what's going on in head, questions like: What would you improve in your life if you could? Is there anything you have on your life's bucket list? Is there something I'm not doing that you want me to do? What do you think could use improvement in our marriage?
So that it's just not you planning date nights, tell him how you want to alternate date plan dates, so if you do it monthly, month 1 will be your plan, and the next month it'll be his month to decide. Try to mix things up when at least you plan, instead of the same old dinner or a movie. Like bowling, miniature golfing, paint and sip class, dance lesson, cooking lesson, picnic in a park.
I have a friend who established one night a week without electronics: no phones, no TV. I'd ask that of him, although a think music would be okay. When the kids go to bed, make them your time together in the living room to listen to music and talk and maybe give each other root rubs or back rubs. I'd say that you take a break from initiating sex, but do keep that physical connection alive with the massages and holding hands and caressing hair.
But yeah, if you give yourself time to see if these changes and conversations lead to improvements or not, you can then make your next decision based on if the outcome is good or bad. Good luck and let us know how it goes.