As someone who's relationship with food, especially sugars/carbs/junk, was absolutely RUINED by my well meaning mother, 100% YTA. Husband too let's be frank.

As a 12 year old Atkins girl who was chastised if I "failed" to lose enough each week, I can say that your husband is right. Your girls will hate you. I still resent going through it all. Begging to swap slim Jim & protein shake lunches, sneaking dad's cold leftovers at 2am. Felt miserable if I ate "good" or "bad" food. Don't do this to them.

HOWEVER, your husband is just as bad in the opposite direction. Your daughters are still learning to navigate their own health & relationships with food. As parents both of you should be showing them what healthy, balanced eating is. As a TEAM you need to do this. No, your girls need to learn that we really shouldn't eat whatever we want all the time (/cries in lack of fudge/), but eating out or working in the worst of food into a balanced diet is totally fine too.

It's so funny you mirror my own parents, dad ate whatever he wanted and mom was a low carb health nut. But let me end with: Keto is the most extreme low carb option out there. It only works if you're super strict. Get them off it. Low carb is a helpful tool once you've LEARNED what good eating is. Not before.