Of COURSE your eldest daughter won't be seen with you in public - but it isn't the kilt. It's 'DAD" that's the problem. Teenage daughters are mortified by their fathers, even by them being in the same room, let alone being 'oddly' dressed.
Dad's are embarassing in a suit, shorts & T-shirt, overalls, swimming trunks,(God forbid!), jeans, whatever. (It's part of the joys of fatherhood to be a source of total embarrassment to one's teenaged children). However, in a few years time, you'll be back on the A-list once more. Cheer up.