Your DH is at fault here.
If he had gone to court 6 years ago, he could have maintained contact and the likelihood is that would have been on a schedule that worked for him.
Now, he could go to court and try to get an agreement, but with his eldest being 16, they could just reject him anyway.
If he is in the situation now where the kids want to see him on a Saturday, for example, and to do this you are going to need childcare for your kids on a Saturday so you can work, your DH can arrange this.
He has a duty to HIS (eldest) DC, which he has very much failed at, to care for them and build a relationship with them, but also a duty to his (younger) DC to ensure they are cared for when you are working and he is otherwise occupied.
Let him arrange childcare and child visitation and step back. You are working, this is not your problem to resolve. It's an issue of your DH's own making, he should not have ignored his kids for SIX years; what kind of shitty father does that??
And why did you think "this seems an excellent man to procreate with, he sees his children as much as a father that's dead 🙄"