Well, I would consider my DMiL to be one of the classiest ladies I have ever known--and SHE was earing just a tank top (and bra with clear straps) as a top out to tour castles on Monday (it was HOT). She is 66.
DD12 wears tanks all the time in the summer. She is not yet interested in boys (I keep expecting it to happen)--though they are interested in her (she looks 16-20 no matter how she dresses; 5'6", curvy as heck, more serious personality). She would rather the bra straps not show--but that is near impossible with a tank and she NEEDS a bra. Her school has no restrictions on this so she can and ocasionally (when it is very hot) does wear them to school. The "look" she generally has when she wears a tank is "sporty" not "sexy" and it has never bothered me or DH. Honestly, since she is not trying for sexy and is just going for comfortable.
Most of her friends wear tank tops. Many much shorter and tighter with lots of sparkles, etc., and paired with short shorts with writing across the butt, etc. DD looks conservative by comparison.
Are you really SURE you wll not be okay with tank tops IN THE HOUSE when your DDs are older? If that is really going to be your hard and fast rule forever then go ahead and enforce this now (no flames from me at all if htis is your belief). BUT, really the only people I know who do not allow them in their own homes on hot days are people whose religions specifically prohibit doing so. I think it would be very bad for your relationship with your SD if you make her cover up in the house now and then let her little sisters wear tanks when they are older. I can see insisting she cover up when you take her out somewhere (shopping, dinner, etc.) but within the privacy of her home I just can't understand that personally. Even I wear tank tops to clean house, do yeard work, etc.

If you
ever do that I really do not think you should enforce the rule (just my opinion).
As far as your husband goes. Maybe it would help them to have good one on one time (as you would like them to have

) if you arrange for some special outings. Dad's often are not so good at the planning stuff. Maybe if you see that a musical is in town that she would want to see (even at the local high school) maybe you can buy tickets for just the two of them and suggest he take her for ice cream after the show, or buy movie tickets, etc.
BTW--I think it is fantastic

that you seem so concerned and care so much about your step daughter.