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It is not so much a matter of being controversial. The current description will be difficult to publish because it is impossible to understand from it what exactly the rules are. For many of the sentences you wrote I have no clue as to what they mean, if indeed they do mean anything at all. For example:

The Queen can be in check too.  

Yes, and? Must it move out of check in that case, can it move into check?

One of the unique features of Dating Chess is the "attraction power" of each piece. Each piece has either a "+" or "-" sign underneath it, representing its "attraction power" on a 50-50 ratio for each army.

Is this information hidden from the players until the pieces get involved in a capture, or can they peek onto the bottom of a piece any time they want? How is the assignment of the +/- decided? Do just any 8 randomly chosen pieces get a +, or must the + signs be evenly divided over the various piece types?

The person with the "+" sign becomes the head of the family, and the other person switches sides.

If there is no normal capture, then what does 'check' mean in the first rule above? If a single + King is attacked by a - Knight, is it in check? What if the King did manage to become part of a family: is it in check when a Knight 'attacks' it (i.e. could have moved to the same square if it had been empty)? Or can only a Divorce Lawyer check it? Can a King labeled with - capture a single enemy piece? What happens if that piece turns out to be a +, so the King now flips side in the resulting family?

They continue to remain both on the same square and can move as either one or the other piece that form the family.

So what happens if the capture was en passant? Do attacker and victim still end up on the same square, and would that the square of the attacker, or the victim, or the piece marked with the +?

In that case, the Queen will "fall in love" and agree to "forming a family" by jumping across the board in the same square with the King.

What is the point of that? The game is already finished at that point, right? So who cares what goes on after the game?

The political landscape of the game is also determined by the ratio of liberal/conservative families on the board.

What decides if a family is liberal or conservative, and have all families to be one or the other, or are there neutral families too? The concepts liberal and conservative have not been mentioned at all. What does 'political landscape' mean here, and why should anyone care what it is?

Any enemy piece in the King’s or Queen’s range, upon capturing, can become the new Queen or King.

Upon capturing??? Does that mean when it captures, or when it gets captured? What does 'getting captured' mean here anyway? Is the piece that remains stationary captured, or the piece that flipped color (which could also have been the moving one, if it was labeled -). Does this also apply to pieces that were 'expelled' because of a non-match? What does 'new King or Queen' mean here? Does it get a King's move (in addition to the move of the piece it was paired with)? Or does it keep its move, and now is royal? Would it still win when it entered the opponent's territory as part of such a family?

In that case, the other “single” royal figure on the board becomes vulnerable and can be checkmated.

Checkmated? Can it be checked, then? Or do you mean that it can be captured (whatever that means), and is under no obligation any longer to avoid that?

The King wins if he can enter the Queen's territory.

Can it move into check when doing this? (Whatever check means...)

The King is by default conservative, while the Queen is liberal. 

By default??? So it can also be different? Under what circumstances? Before, you mentioned families could be conservative of liberal. But single pieces can apparently be that too?

If the head of a family decides to self sacrifice in order to save his/her own royal figure, the family is spit up and both pieces will return to the original owners.

Split up how? When a player decides to do this, where would the pieces be located afterwards? What is considerd 'saving its own royal figure', that apparently is the condition for being allowed to do this?

The White King can still lose the game, even after "marrying" the Pink Queen, or another Queen, if the liberal/ conservative family ratio is too unbalanced on the other side. 

What is considered 'too unbalanced'?

However, a newly formed royal family may count as two ordinary families from the board. 

A 'royal family' is a family where both pieces are royal? Not just one?

In summary: almost nothing is clear. The whole description utterly sucks. That has nothing to do with the game itself, which people might actually like, if they only could understand how it has to be played.

Also note the diagram you show does not correspond to the setup you describe in the text.