G.B.
I don't understand your question. You can't just up and decide to adopt someone else's children. The mother has to give up her parental rights and allow the adoption. Unless she does this you cannot legally adopt these kids at all. Ever.
You need to contact an attorney and file the proper paperwork to notify her that hubby is seeking to terminate her parental rights and that will mean a lot of things to her. No more child support if she was even paying any to begin with, no more visitation ever, well, until they are 18 and choose to look for her on their own, and the possibility of never seeing them again at all.
I would think if she has any desire to be their parent she would have at least called or sent a card or two to them. It really needs to be fully something they want but I would never never never even approach the idea with them unless the biological mom was on board with the idea. They need to visit with her so they can hear her thoughts on it and know she is okay with it.
If the mom is incarcerated or in rehab, something like that they may not even let her discuss any legal changes until she is out. That could come back in the future to bite you guys in the hiney. She could say she had no choice about it and she was coerced into signing away her rights.
She must be contacted and ads ran in the newspapers, relatives contacted and instructed to let her know there is going to be a hearing about her parental rights, etc....you do not have any custody or guardianship, legally, but hubby can sign papers at each medical facility such and the pediatrician, the health department, local hospitals, ect...they will each have their own form plus probably a Notary to make it official, then he needs to do this at the schools and even at the Administration building of the school system. This way is something were to happen to him they would know you have his permission to act in his absence.
If the kids are not on board you should not adopt them. It would not be to your benefit to do so. They would resent you for the rest of their lives and would turn their backs on you as soon as they were legally able. Make sure mom talks to them to let them know it's okay with her so they will be more excepting of this transition. You can't just step in and say "Oh, by the way, I'm your new mom now".