Hello again Dan --
In order to obtain a custody order in this situation you are going to have to file for custody in the clerk's office of the county family courthouse where your daughter is living right now. In order to gain custody of your daughter, the Judge will have to find that it is in the "best interest" of your daughter for you to have custody at this time in her life -- that is the legal test -- it is actually called the "best interests" test. To determine which parent should have custody under this test the Judge will weigh a number of factors affecting your daughters life as follows: (A) parenting skills of each parent (B) stability and emotional maturity of each parent, (C) ability of each parent to provide a stable home (which is more stable?), (D) is there extended family support with and around the parent who seeks physical custody (grandparents, aunts & unlces, etc), (E) any educational needs of the child and has the child started school and made friends, (F) if the child is in counseling and what does the counselor say, (G) if the child has medical needs and which parent is better able to meet them, (H) which parent is better at and more open to facilitating the relationship between the child and the non custodial parent, (I) and then any other factors that the Judge deems to be relevant in this case (I believe that the fact that mother moves around a lot will be a factor in this case when you bring it up to the court). If the parents are unable to agree and the Judge wants more information to get more familiar with the family, the Judge can appoint a Guardian ad Litem (GAL) -- and the GAL is a lawyer or psychologist who goes out and interviews relative, friends, counselors, doctors, school officials and both parents and the GAL will make a recommendation to the Judge of what the GAL believes should happen with the custody situation (either parent could also ask that a GAL be appointed to investigate these matters if the Judge does not do it on his/her own). THe GAL will also be instrumental in setting up the visitation schedule for the non custodial parent once the final custody decision has been made.
So, if you believe that you can pull some proof together that your daughter is better off on a number of points if you have custody of her then you can and should file for custody --- and even if you are not awarded primary care of your daughter, the best thing for you to do under the circumstances that you are in now (Mom wanting to move 3200 miles away) is to get this matter into court on the custody hearing because you can get a court order that states that Mom is not permitted to remove Bella from the state she is living in now (or your state) without your express written permission or the permission of the court overseeing the case. If Mom ignores such an order and leaves the area with your daughter anyway then you can go right back to the family court Judge with a COntempt of Court complaint and you will be awarded primary custody of her -- and then armed with the custody order you can go to wherever she is living in the US and get the assistance of the local police to get your daughter (because all states must acknowledge and follow court orders from every other state). With a little luck, if Mom knows the serious consequences of leaving the area with her then she will not do it without permission from you or the court (if she seeks court permission she must show that the reason she is moving is for better employment or that she will have stronger extended family ties in another state -- and she would have to prove these things to the judge and work out a long distance visitation schedule with you before she would be given the permission to move a long distance away from you).
So, you need to go to the family court (clerk's office) and ask them for the form paperwork to apply for custody of your minor child and you can complete the paperwork, file it and ask for a hearing date -- you will then have to serve the paperwork with the hearing date on her (use a SHeriff to do it in the county where she lives) and simply wait for the hearing date and appear. In the paperwork you should write that you are seeking primary custody because it is in the best interests of your daughter at this time to remain living in Maine with you, or in the alternative, you seek liberal visitation rights and an order of the court that Mom cannot take the child from the state without the permission of the non custodial parent or the court. You can also hire a family law/custody attorney to do this -- but you will need to contact the county bar association in the NH county where she is living and ask for a referral to such a lawyer to handle the matter for you -- they will refer you to several different lawyers and you can talk to each and make a decision on who to hire -- if anyone.
I hope that helps and answers your questions.