That's the idea of the Federal Marriage Amendment. It seeks to limit activist judges from messing with the definition of marriage. Instead of amending an amendment, there's not problem with adding a new amendment. Same difference.
You probably could fit this in the bill of rights, something like the right to be a normal heterosexual.
There is a big difference. The amendment they want to add places a rule on the citizenry. But, instead of adding an amendment, they can amend the existing article or amendment to clarify its intent while not changing the direction of authority (the direction of authority of the Constitution is to place rules and limits on the government, not to place rules upon the citizenry from the government).