Since nothing ever happens without taking initiative, here a draft bill.
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Draft Bill Proposal
International Divorce Immigration Relief Act (IDIRA)
The purpose of this law is to allow children regular, meaningful contact to both parents, also where families become separated over international boundaries in times of globalization. It also improves the ability of parents to financially support children legally residing in the United States, for example, allowing a parent living in a underdeveloped country with low pay to help in the upbringing of the minor child.
Definitions: Eligible Visa Applicants are:
Biological or adoption parents of a minor child, if
a) the child, as well as the custodian or parent living with the child, are US citizens or long-term permanent residents or non-immigrants lawfully present in the United States
b) the child was born to, or adopted by the applicant while the applicant was lawfully present in the United States as a long-term permanent resident or non-immigrant visa holder
c) the marriage resulted in divorce or separation with the child legally remaining in the United States
d) the applicant left the United States according to immigration law and was not deported
The parent or custodian residing in the United States with the minor child may not have to be a US citizen.
In addition, a parent of a minor child if the child was born or adopted into the family outside the United States but where one custodial parent (whether US citizen or not) has since lawfully relocated with the child to the United States, is also eligible.
Terms of the visa:
The visa is for three years, indefinitely renewable until the minor child reaches age 21. It allows unrestricted, yet temporary work in the United States and the accumulation of social benefits. Child support as ordered by family courts will have to be paid or the visa may be revoked. The visa holder is considered a potential legal immigrant and may switch to other visa categories and apply for Green Card, e.g by self-sponsoring. If the minor child has left the United States permanently or reached age 21, renewal is not possible.
When the applicant files for this visa, immigration officials will check the immigration or citizenship status of the US-residing custodian and the minor child, as well as divorce documentation. If the parent or custodian lawfully residing in the United States has unlawfully taken the minor child to the United States (kidnapping) and if that person is not a US citizen all immigration benefits may be revoked and that person may have to be ordered to leave the United States to the country where the applicant resides. This may be waived if not in the best interest of the child. In the latter case, the new parent visa shall be granted to the applicant.