I get your frustration, although on a bit lower level. Hubby is somewhat the same but not quite as bad. To me, it's mostly because he's not here as much as I am or as involved with the animals as much as me. He won't 'follow through' sometimes, as I would. And he's just not as observant as me.
And yes, he sometimes let's them get away with murder that I wouldn't. I feel he depends on me a lot when I'm here. And I'm almost always here.

The few times I do go away, like to visit our daughter in Kentucky, believe me, I worry. But I think those times he is much better! Probably because he knows the Wrath that would be coming home if something happened!

He's pretty good about adhering to my rules. Probably because he feels the same. For instance, he would never let Annie on our bed or couch in the family room. She has the sunroom couch and he knows the rules.
Perfect example of not really following through was when we had Buddy. Buddy was attached to me more than my husband. And if we were all outside and I wanted to stay and asked him to take Buddy inside, he would always tell me, he's not going to go with me. And it was true. If he called him, sometimes Buddy would look at him and then look back at me like, no I want to stay with Mom. But I would tell him,
make him!
Make him listen to you! But most of the time he just wasn't that aggressive about it and I would end up taking him in.
Today was another great example. After the Fox Fiasco this morning I had gone out to the barn to feed the horses. 15 minutes later my husband comes out with Annie. I look and she has no collar. No e-collar, no nothing. I told him, "Seriously? There was a fox out here minutes ago and you let her out without a collar?" He kind of gave that look like,

oh yeah maybe I should have. Yeah you should have.

Luckily she was not that interested in leaving us and was playing with her rope. But I want to slap my head like, what were you thinking? I mean she's really good about sticking with us and listening to us. But I would have never taken that chance with the possibility of that fox still being around. Especially when you're not constantly watching her while we tend to horses.
Now your little boy eating everything in sight is very very stressful. It's like you can't take your eyes off him. And you shouldn't. I know how much time and effort that takes. I've done it with Annie. She's not nearly as bad but I'm still very watchful with her.
All that said, I am and always was the main caretaker of the animals and my husband knows it. Even if he doesn't train them or follow through on some things, he's pretty good about keeping my rules. You can't be giving mixed signals to the animals or even the kids! But at least with children they understand what you're saying and you can explain why Mom and Dad differ on something.
I saw this video going around and have to laugh! Gentle parenting does not always work. With children or animals!