So, you've been through the ordeal of a custody battle, and lo and behold, you were granted custody. Now what do you do?
Get them involved right away in new activities. Get school aged children in school right away and take your children to church or other places where they can make new friends and where they will stay occupied. You may consider pre-school for a younger child. Try to get to know other parents and have their kids over often.
They will be most homesick when bored, so you want to try to avoid that. Young children like to be helpful, so letting them help around the house also makes them feel like part of the family. Older children will also adjust more quicly when they take on some responsibilities, but you have to be even more careful to praise and thank them, and to be very careful and tactful in how you ask for their help. If they haven't had much responsibility in their previous household, they may feel like you are taking advantage of them. Children can help with vacuuming, dusting, shoveling snow, gardening, emptying the dishwasher and other easy chores (with younger children it is quicker and easier to do it yourself, but better for them if they do it with you). Make them feel like they are contributing to the family. Make sure you THANK THEM AND PRAISE THEM for what they do!
Don't forget to set aside one evening or weekend day each week for "Family Time". The TV stays off during this time. You play games together, go bowling together (some bowling alleys have bumpers they can put in the gutters so young kids don't get so many gutter balls), or make cookies for the neighbors (it makes a mess when young kids help with that, but they really enjoy it). There are many things you can do. This is a time for bonding.
Go easy on the discipline at first, but make the rules clear. Kids appreciate freedom, but they also grow from and appreciate realistic limits. They are going to feel overwhelmed at first, so the quicker you get them into a routine, the better. Be extremely cautious, however, that you don't expect perfection from them. Allow them to grow one step at a time. Pick your battles, and let the unimportant stuff wait until the critical stuff becomes habit.
The worst of the homesickness will probably pass after the first 3 weeks or so. Contact with their bio-mom can extend this indefinitely if she doesn't cooperate. Make sure you send her drawings from the kids and pictures. Let her know you still support her as a mother, even though you felt you had to act in the children's best interest. The quicker she heals and realizes the children are happy and healthy, the better for everyone. Some people never do heal, but you should try to be helpful and understanding. Don't give her more reasons to hate and fester.
If there is some distance between you and bio-mom, it will help keep her from smothering the kids and keeping everyone miserable. Limit her phone calls to 3 times per week or less (depending on the children's reactions), though they can be as long as she likes. If they get off the phone and don't cry then or when they go to bed, you can allow unlimited contact. If they whimper for a long time after each contact, then ask the mother to give them a little time to get used to the situation and limit her calls (consult with a counselor or your evaluator first), but make sure everyone knows this is only temporary. Like I said, the children should adjust, for the most part, within about 3 weeks.
There will likely be occasional incidents of homesickness for quite some time, especially after any discipline, so make sure you criticize what the children do, not the children themselves and that you temper any discipline with lots of love, encouragement, and appreciation/gratitude for their accomplishments and help. Encourage the bio-mom to tell the children she loves them, but not that she misses them. It can make them feel guilty for being away from her.
You have a big advantage if there is more than one child. They will keep each other company, but expect occasional radical behavior from a younger child when the older is in school, plus they may fight a little more than usual. Pre-school will help with this to some extent. The most important things you can teach them now are that they are loved and that they are an important part of the family. Give and expect lots of hugs. They are the best medicine. If they are hostile or uncomfortable with hugs, don't force the issue, but find other ways to let them know you really care (like taking the time to read to them or go to the park with them). Your time is the greatest gift you can give a child.
It will be an adjustment for all of you. There is nothing more frustrating than a small child who will not stop crying or whimpering, but nothing more rewarding than a child's smile.