Article 4, Section 2 is a rational choice of law in Any conflict of laws under the authority of the United States.
Here's what that says (I'll provide the text and the link when y'all won't)
Article IV - National Constitution Center
SECTION. 2. The Citizens of each State shall be entitled to all Privileges and Immunities of Citizens in the several States.
A Person charged in any State with Treason, Felony, or other Crime, who shall flee from Justice, and be found in another State, shall on Demand of the executive Authority of the State from which he fled, be delivered up, to be removed to the State having Jurisdiction of the Crime.
No Person held to Service or Labour in one State, under the Laws thereof, escaping into another, shall, in Consequence of any Law or Regulation therein, be discharged from such Service or Labour, but shall be delivered up on Claim of the Party to whom such Service or Labour may be due.
So the privelege of marriage shall be extended to any conceivable combination of consenting adults. Children too I suppose, since they also are citizens. Right? Or are some more equal than others?
The problem you are going to run into is that each state gets to define marriage. Then, once defined, all people in that region may enjoy that definition. It is also a privelege to drive, but doing so while legally blind means you will cause harm to others while driving. Being of the same gender "as a couple or group" means that you are not going to be doing parenting adequately. So your "union" will cause harm to others: namely children who depend upon marriage meaning "both adult genders as parents/role models", not just one of them.
Consult the Prince's Trust study for details.
http://www.princes-trust.org.uk/pdf/Youth_Index_jan2011.pdf
FROM THE PRINCE'S TRUST STUDY:
Page 8 (the left side on the green background)
In addition to indexing the happiness and wellbeing of young people, the report explores some significant demographic differences between young people. They include a comparison between those not in education employment or training with their peers...those without a positive role model of their gender in their lives (women without a positive female role model and men without a positive male role model) and their peers...those with fewer than five GCSEs graded A* to C (or equivalent) with their peers... Respondents are asked how happy and confident they are in different areas of their life. The responses are converted to a numerical scale, resulting in a number out of 100-- with 100 representing entirely happy or confident and zero being not at all happy or confident.
Page 10 (The bold largest heading above the material that followed it)
Young people without a role model of the same gender in their lives
Children have civil rights too; perhaps the most important of all since they cannot vote to affect their circumstances. They aren't possessions or slaves that are "of a secondary consideration" when defining marriage. They are in fact the primary concern of marriage.