TK business booking classes are C D Z K J
Not sure where you got F from.

1400 for a US-EU business return is a smoking deal! I doubt you’ll get anywhere close with a rebook, especially if you’re looking at peak times or short notice.

Bite the bullet and spend the additional 1800 if you can afford it or see if you can rebook to economy and not pay more.

But above all, enjoy your time with your kids. You can always earn more money.