Depends on how "black tie" they are making the occasion, I did some googling a couple of months ago when we were invited to a dinner where dress code was strictly black tie.

DH wore a suit he had which is dark grey with a white shirt & black tie. I wore a dressy ****tail length dress (just below knees) and neither of us looked or felt out of place, if anything this was kinda the norm of what everyone else were wearing. There were some in tux & long dresses (mainly older). So what you already have will probably be ok.

I suppose putting black tie on invites discourages jeans/more casual type clothes.

Kids are probably required to be dressed kinda formally boys in pants, shirt and girls in formal party dress - could you possibly hire something for them?