Dache, I've never prepared meat in my house. OH wasn't vegetarian when we met but since we moved in together (14 years ago!) he hasn't eaten meat at home, and rarely when we were out together. My attitude was that he could buy it and prepare it himself if he wanted it, clearly he didn't want it. He has eaten meat occasionally with his mother, but has now moved away from that entirely. He isn't one for labels, so he wouldn't call himself vegetarian, effectively he is though.
It's a different situation if your DH is a committed meat eater and thinks your daughter "needs" to eat it. I don't think she does, and lots of people agree, but you and DH need to work it out between you. You will also need to research your daughter's intolerances - if she is lactose intolerant, Ali is right to say there are lots of lactose free cheeses, milks, yoghurts available, and tofu of all sorts, as well as nuts and beans and lentils and eggs! If it's MPSI, it's another story entirely, it's far more restrictive. Again as Ali says, it might be good to look at vegan diets, just to get to started thinking about it.
imagine him deciding not to eat fruit or veggies.
This is not really comparable - there is no ethical reason for not eating fruit or veg.