It is extremely likely that the court would grant you access with your sons as long as there is no history of abuse or neglect. You should consult with an attorney, who can review the current custody order and better assess the facts of your case.
No, your former spouse's remarriage is not considered a change in circumstances that would justify a recalculation of child support. The reason behind this is that your former husband's new wife does not have an obligation to support your child.
You should be able to resume use of your maiden name based upon your judgment of divorce without any payment of filing fees or court involvment. You will need to produce copies of your judgment of divorce for the DMV, Social Security, your bank, etc.
Assuming you have an order of child support, you should file a petition for enforcement and/or violation of that order. Based on the facts you set forth, your child is not emancipated and his father had no right to unilaterally start paying support for only child.
In addition to the suggestions you have already received, you may want to contact the lawyer who represented you in your divorce. Depending on how much time has passed, your attorney may still have a copy of the judgment in his or her file.
Bring copies of your judgment of divorce and any paperwork related to the pension and life insurance. Listen carefully to the questions that the attorney asks and answer only that question without giving a lot of extraneous information.
If you have an order granting you access with your child, you can enforce that order. You may also want to consider petitioning to prevent your child from moving away. You should consult with a local family law attorney to learn more about your rights.
You may be entitled to modify your access schedule based upon the other parent's violation of the agreement. You should consult an attorney to discuss your situation in more detail and explore your options.
Assuming that you have primary residential custody of your children, you will be entitled to receive some child support from their father even though you earn a lot more than he does. He is not exempt from paying support because he earns freelance income as opposed to wages or a salary. The amount of support will depend upon your respective incomes. You should retain an attorney to commence a support proceeding on your behalf as soon as the twins are born.
A father cannot unilaterally...
You should retain an attorney to prepare a petition on your behalf for a holiday schedule. The Court will most likely order holidays to be equally divided between the parents, with a specific schedule set forth in the order.