So, if you have holiday for a week, or had to go off sick for a few weeks for surgery, they'd manage. No-one is completely indispensable, and the world will indeed turn without you, no matter how it feels now.
In my old job, I made a request in 2019, to WAH one day per week, for health reasons. It was turned down by my arsehole old boss, who said I couldn't manage a team remotely. Then lockdown happened, and we all managed it remotely (really well!) for about 18 months in total, so he was proven completely wrong. So, you can manage it. If your team aren't able to work without you there, you have a problem with how you manage, and how things are set up, because even those on minimum wage jobs (no slight - I've done these!) can manage a few hours without constant supervision.... and what happens otherwise when you need/want time off?
As a Manager, if you came into a meeting with me, with all of this minutiae, I'd be saying 'you maybe need to think if this is the job for you.' However, if you came with some reasonable suggestions, I'd do everything I could to work with you and find a solution. I think you either need to pay out some money for a Nanny, no matter the cost (because you'd be financially worse off with no income!), or look at changing your hours. You could potentially make a case for starting earlier, and your husband doing drop offs, so you could be there to do pick ups - which is an arrangement a lot of friends and colleagues have done. So, one of you works 07:00-15:00, and does pick ups; and the other works 09:30-17:30/18:00, depending on your hours to be worked in a week. Also, your hours don't necessarily have to be the same each day, surely? Why couldn't your hours be different on the days you're WAH, for example. Go with some options for solutions, not just problems.