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DD is still using both hands, but i always pass into her right hand, to encourage right-handedness (if she's left-handed i can't change it but if she's between the two i can),

Really? Why?
Because it's easier and safer to be in the 90% of people the machines, roads, equipment and ways of doing things the world is set up for, primarily and also a little because the way a left-handed brain processes information makes learning a less flexible affair. It's incredibly handy to be left handed if you're in a car crash because things like motor and language skills are more spread out, over both hemispheres (rather than in one hemisphere) so you're unlikely to have more devastating effects from head injury, but equally you're more likely to be in a crash if you're left handed because the cars and roads and other drivers expect you to be right-handed.

I have nothing against left-handed people, but i think for her sake she'd be better off right handed IF she can choose. If she can't of course that's perfectly fine too.

Bx