OK, to startwith, I would go cold turkey on the milk right now. Offer her a sippy of water when she goes to bed and show her where it is so that she can find it easily.
with the sleep training, you are on the right track with staing with her and moving towards the door, perhaps you could try put down and walk out. As hard as this is going to be, you have to do it at bedtime, nap time and nightwakings in order to be consistent. If you do it, then go back to laying next to her it will only prolong the problem and she will realise that if she tries hard enough she, Mummy will come back. Also, she needs you to fall asleep, so when she wakes at night she needs you (or milk) again. She needs to be taught to sleep independantly.
what is her daily routine.