He was too old when he had kids. Stuck on Single Selfish Mode for too long. Now doing anything for anyone else feels like an unreasonable burden.
Ding ding ding
That's just another excuse. DH was mid 40s when we had kids and he routinely cares for the entire weekend days, longer when I travel. Sure, he's tired but he is capable of parenting.
Op I would go to marital counseling or solo counseling. I would also tell him that his wife deserves an equal partner and his kids deserve a capable committed father and he no more deserves free time than you do.