Dual Military with a kid from previous marriage and one with current marrige. Do both kids go on both FCPs or just the actual parent FCP?

AR 600-20 Army Command Policy paragraph 5-5 a(2)...take a look at the attached documents and be sure to read the rest of the regulation it may help you a little more with the answer you are looking for

BLUF: If it is important than it would be written down. There must be some sort of court order or adoption document that states who's kid is whos.

Likely his biological mother is the provider.

IAW USAR PAM 37-1 para 3-19 (Note this that is USAR only):

Dependency determination. The unit commander or alternate certifying officer determines entitlement to BAH with dependents through a review of dependency documents such as marriage and birth certificates, court orders, divorce decrees or child support orders. Dependency must be certified and approved before authorizing entitlement to BAH. Certification and approval is accomplished by completing a DA Form 5960 or DD Form 137–3, -4, -5, -6 or -7, as appropriate, and DFAS 27-41 to document the Soldier’s dependents. The appropriate form is determined by the relationship of the dependent to the Soldier. See table 3-1 for dependent types, supporting documentation, approval authority, and appropriate forms.

You can also e-mail [login to see] , DFAS will determine if the Soldier is eligible for BAH on behalf of the dependent and return a DFAS Form 27-41 to the Soldier. Create a DA 5960 in RLAS once you have the approved DFAS 27-41. Place a copy of the DFAS Form 27-41 in the Soldier’s Military Personnel File (MPF) and upload the DFAS Form 27-41 into IPERMS.