Not heard the broadcast but WTF???? My gorgeous DD refused to wear a dress / skirt once she got to age 4 as it stopped her playing - climbing trees, playing football & running around with her cousins. She had dolls but the lego was mainly that aimed at "boys".
So, had I been this parent, I would have been asking her if she felt more male??? She's still happier in jeans and trainers than in a dress and heels - so much in fact that I nearly passed out in shock when she asked for both to go to an upcoming wedding. And yet this is still the girl who is happiest on a football field or watching the red arrows.
Supporting your child is one thing - but asking about their sexuality - at 10 - is a bit nuts to say the least. Yes, one of DD's male friends came out as gay in year 8 and another (female) wonders if she is bi, but in both cases, the parents just said "well, ok, that's how you feel now, see how things develop".
Once older, if the person is truly trans, then that's fine - trans men / women have gone through a lot of soul searching before transitioning into the person they truly are, so deserve our support. Maybe this child will transition when older, but being forced to decide is just wrong.
And Unicorn you sound truly supportive, I hope that things are better for you and your child and that they find the peace and identity in which they are truly happy -and that you also are able to find comfort once this is complete and you have your child back, in whichever gender that turns out to be.