You will find that TK *G doesn't get you much on LH. No bonus miles, no seat selection, no luggage. Just lounge access. You won't ever get to TK elite status on just LH short-hauls either.

Travelling to US/Mexico via IST is something you will do with the family maybe once in Y and a couple of times in J before your better half vetoes all the extra flying hours

Using TK miles on partner airlines is a nightmare.

Although obscure, you might want to look at the Egyptair programme. AFAIK their family account means that everybody's travel counts for the lead member's elite status.