This is a dichotomy. Both things cannot be true.
No, I disagree with you about that. I don't think that those who signed the Declaration of Independence meant that if 3 out of the 4 families living on your street want to form an independent country, that they have a God-given right to do so. That fourth family has rights that you are ignoring.
I recognize that you don't mean one street, but the principle remains the same whether you're talking about your street, your village, your county or your state. You're going to need to work out these issues with all of us. If you could make out a convincing case, it could probably be done in some way.
If your objection is to a required size of the population, then I will put your concerns to rest. The Southern population was larger than the population of the Colonies when the Colonies left the British Union.
If your objection is that the desires of loyalists ought to override the will of the Majority, then I ask you what is your position in regards to the British loyalists when the colonists broke from the British Union?
This sounds like another example in which both positions cannot be true.