1. The father of an EU citizen child, such as your child born in the UK has the right under the Zambrano decision of the European Court of Justice to both live and work in the UK or any part of the EU to support that child.
2. This zambrano right is not dependent upon showing that he or his dependents earn any set amount of money. So, it avoids the difficulty of you not earning in the necessary GBP 18,600 in order to gain his entry. Accordingly, I would suggest you get a passport for your UK born child AND your other child (who would be entitled to it by descent because of your british nationality) and the exercise the Zambrano right to bring in your husband.
3. In essence your husband is entitled to a derivative residence card as he is the father and carer of his UK citizen child. here is a link to the UK Government website for the derivative residence card https://www.gov.uk/derivative-right-residence/overview. However, he can also apply for Further Leave to Remain (Family Provision) - FLR (FP)
4. If you want any further explanation, I will be happy to assist further. However, you should look up the Zambrano decision on the internet and understand it. It holds the legal basis for your husband to join you and your children in the UK.
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6. It is not an EEA family permit. It is further leave to remain based on his parentage of his child. He should seek to apply as parent of the child, not as your spouse.
7. I don't know where you are getting that you cannot apply until the child is 5. That is an incorrect interpretation of the law I have set out for you. Secondly, he can certainly apply even though you will also be looking after the girls. Finally, I don't know why you think he should apply for another visitor's visa when he can get a permanent visa. That is foolish.