OP i think your ignoring the bigger issue here which isnt a criticism its probably just not crossed your mind.
The issue here is:
Why is he not an enthusiatic parent?
Children are not burdens or a job. Its a whole lifestyle you take by choice. Its a lifetime vocation. Yes its hard but the whole point in going out to work and everything else should be about the its all a means to an end for your KIDS. You work mon-fri so you support your kids. You have weekends off so you can spend time with your kids. You come home from a long day of work to be with your kids!
The only analogy/metaphor i can think of is:
Imagine you are not particularly interested in dogs. You like the idea of a cute dog to cuddle on the sofa. But that's it. However whenever you come home from work your expected to have to walk your dog. In rain or snow or sunshine. Then your expected to clean up dog poo. Then make its food. Take it to the groomers. Have it chew through your beloved possessions.
Someone can give you a book on dogs, someone can give you the best leads, dog beds, food etc. But ultimately your just not fussed with dogs. You dont want to go to petsathome at lunchtime. You don't want to get up at 6am to take the dog on a hike. Because your just not fussed on dogs. Its not your thing. You can't force it. You know the dog needs these things so you go through the motions but ultimately you can't be enthusiastic about something you have little interest in. It would feel like a burden.
Now a dog lover would see all those things as fun. Taking the dog on a hike and coming home to their pup after a long day of work would be their highlight. Because they love dogs. Have an interest. Chose to have a dog. Infact they have 2 dogs. They centre their lifestyle around their dogs and dog holidays and go places suitable for dogs at weekends. Through CHOICE. They enjoy it. They dont care about the poop or rainy walk. They adore their dog. They WANT to spend time with their dogs.
It would be madness to expect someone who isnt bothered with dogs to feign enthusiam and interest in dogs and sacrifice their entire lifestyle to a dog and be happy about it. It would be crazy to expect them to voluntarily take the dogs for a walk in the woods everyday of their weekend. Yes they may do it when pushed but they won't enjoy it the same way a dog lover would. It would feel a burden.
Infact if someone you know got a puppy who doesnt like walking, dogs and smells, you'd be wondering wtf their thinking?!
Now replace dogs with children.
Either you WANT to do it or you don't. Simple as that. Yes you can compromise and discuss. Yes he may even become reasonable and spend his time with the kids. But if he doesn't feel it he doesn't feel it.
He'll be doing it because he feels he HAS to and not because he WANTS to. That is the core issue of it. You want him to WANT to do those things. Not do it out of obligation.
I dont think you can force those feelings. So either you accept this is how it is. Hes just not interested. He doesn't feel the same enthusiatic way about the kids OR you leave him because deep down inside you know hes just not bothered and thats a deal breaker for you.