Oh op, you sound exhausted.
Life is not fair...fact.
You are right in everything you say, unfortunately you met an incredibly selfish human being and had children with him.
I understand you need physical and emotional help with doing what is considered the hardest job you will ever do, rearing children, it's a dilema, you need the help and you want for your children to keep in contact with their father, but it shouldn't be your further job to badger him to have his own children.
As if your life isn't hard enough.!
Could you explain to him that this time as they are growing up is so important to them, to feel needed and wanted, not a burden, it will affect them for the rest of their lives speak adultly to him.
Read up on the affects of abandonment and desertion, present these facts to him, he needs to hear this.
Tell him your'e thinking of taking them to therapy as they are feeling unwanted, that may nudge his guilt, it will be on record he is failing as a parent... official, tell your gp you are not coping well cite the reasons, it is affecting your health.
Why must you suffer in silence?
You need a stronger support system for yourself and the children, he obviously cannot be relied upon, he is a waste of space, do your own family help?
One day his chickens will come home to roost, but that doesn't help you in the present.
The balance is so unfair.
Take care, you are a formidable woman doing this all on your own.