If you make yourself wince, then you can probably fix it. You may never be a wonderful singer, but if the problem is that you hear yourself sounding wrong and don’t know how to do it right, then you can potentially learn how to evaluate yourself reasonably well over and over again as you practice.
If someone else had to point out that your daughter was singing it all wrong, and you’re taking it on faith that they’re correct, you may be hopeless. If you can’t hear the difference between what you do and what everyone else does, how are you supposed to adjust yourself to match?
If it helps, I’ve met very few people who genuinely couldn’t tell. I’ve met a lot more of them who knew perfectly well that they sounded awful, but had no capacity to produce correct notes themselves. One of them was so bad, she could literally only hit one note – the guitar tuner said it was a slightly flat B, if I recall correctly. She took no pleasure in croaking, and simply refused to sing in front of anyone else for any reason, but she could hear what other people were doing right just fine.
Try singing along with something you know well while under headphones, with one pad on and the other tucked behind your ear? That gives you a reference on one side and a way to monitor yourself on the other. The above suggestion of Rock Band is also a good one – the game gives you a visual representation of the pitch you’re singing and how close you are to getting it right.