The decree says her cash comes from your 401(k). Only a QDRO can do that. Your ex will need to pay taxes on the $4,603.50, but she volunteered for that when she said the money had to come from your 401(k). Depending on her tax bracket, there may be very little tax to pay. The upside for your ex is that she doesn't have to pay any penalty.
The biggest problem I see for the two of you is your fight is going to cost more in attorney fees than it's worth. Ask your 401(k) manager for a sample...
Your ex has made the mistake of forcing you to seek legal advice. Take advantage of the delay he is causing by getting educated about your options. It sounds like there is more work to do on your parenting plan. Consulting for an hour with an experienced family law attorney should give you an excellent idea of what the parents and child are really entitled to in a parenting plan and what the process will be to finish your case.
The first two attorneys gave good answers. Of course, not everything is required to go to trial. If you and your husband can reach an agreement, it will make things pretty simple. Just remember that you will need either the court's approval or the father's written agreement to relocate your child out of the school district. You might also want to get advice about whether it would make more sense to give the house back to the bank if the rent you would get is less than the mortgage payment.
If the biological father was confronted with a child support action, he might see some value in allowing an adoption. On the other hand, he might demand visitation, although he would face an investigation over how much contact is appropriate if he chose to do so. You would need an experienced family law attorney to pursue this course.
Typically the cost would be calculated at the same rate she charges for the other children because she is using one of those slots for your child. You may have problems if you haven't complained about this to her previously and/or due to the fact you've waited a long time to take this to court.
Generally, you can't divide what's gone. If $80k of separate property was used for a down payment on a house, then there would be a claim for the first $80k off the top. But if the stock was liquidated to take trips, pay down credit cards, living expenses, etc., then it's gone and can't be compensated. So the question is, "where's the money?"
Your sister hired her attorney, so her attorney is entitled to get paid by her. She is responsible for collecting from her ex.
At this point, your sister has a collection problem, not a family law problem. it appears her attorney's usefulness is done if he or she can't collect from a service member. Most family law attorneys don't have experience with military divorces or collections, so it's time for your sister to switch to one who does.
It's highly unlikely the court would approve this arrangement if it's opposed by the other parent. Even if it's entered by agreement, it would be very vulnerable to modification on an "unworkability" basis or voided as against public policy. How would the inevitable conflicts be resolved? For example, what are the powers of the third party manager? Can they just declare that some expense won't be paid from the fund because they don't deem it legitimate? How will food, rent and utility bills be...
Perjury prosecutions are very rare. To get an answer about the rights of you, your partner (who may have a de facto parent claim) and the bio father (who may have serious problems getting access to the child due to the abuse convictions and his delay in filing a claim), it would be worth spending an hour with an experienced family law attorney.
Mr. Aronoff's answer is correct, but your daughter's situation is not hopeless. While there is no magic age where children get to decide for themselves, a 14-year old who is threatening to run away from her father's must be taken seriously. You really should contact an attorney in your area.