poppyscock I think, all else aside, that you have the right idea. Small tweaks to family life that reinforce your dog's position in the family.
I think we can sometimes be so close to our pets that we forget that they don't have the sophisticated thought processes that we do. So your dog can't distinguish your 15mo giving big hugs and cuddles with her head on him from him giving her a big cuddle with his face on hers.
Your DD will get the rules much quicker. So she can learn that she doesn't put her face near to him. Faces are so animated, and unpredictable. Hands only. Gentle play.
FWIW my parents had a German Shepherd dog when we were small children, and my little sister hit him hard over the head with a broom stick. He was so well trained that he didn't even growl. He did pull her down by her nappy to show his disgust though Most dogs, with the right training, can be great companions for small children. But they need to understand the rules, and the rules need to be consistent.
I know my Westie was hit by children alot in his former home. He can be head shy and gets quite scared. He is very tolerant of my children, but I find that children who visit and don't have experience of dogs tend to ignore warnings. I shut our dog in the kitchen, behind a stairgate, and a visiting child put her face to the gate. I said to come away and that the dog gets scared. I told her not to put her face near the dog. She still did, while her mum & I were stood next to her but distracted in conversation. Her sticking her hair through the gate to him was too much, and he nipped her. Fortunately just a minute cut on her lip.
Whose fault? Mine, and the mum's. I had done everything I thought necessary - put the dog in a quiet space to protect him, and told the child to get away from the gate. But we had got distracted and didn't see that the child hadn't followed my instructions. I now shut him upstairs in our room if children visit, to protect him. I am not putting down a dog because children can't respect his space and I am not willing to take the risk that a child will get hurt. I also know that whatever the cause, he would get the blame.
But my children have known as soon as they could touch a dog that we stroke with gentle hands, and leave him alone if he is sleeping.