So recently built the falkreath house and i got all wings built, even have bedroom for my child on west wing. But when I say let's move to my child it just says "nevermind" as an option while I try to move them from my markarth home to falkreath one. What's the deal?

Your character is not married? I would have thought the children move where ever the family moves to. Or maybe your new house is not ready.

Just fus-ro-dah your family across Skyrim and right into their new home. This will also give your children a preview of possible punishment if they misbehave, so nothing but good things can come from fur-ro-dah'ing your kids!

I've been out my back garden ( in real life obviously ) practicing my Fus Ro Da against squirrels and birds etc. I'm no good at it.

To be able to get kids to move there you need to have built both the child beds and the child chests.
If you don't have both the option to move won't be available