My first question is: why are you trying to get her to drink milk if she doesn't want to? Many mental issues with food arise when parents force their children to eat certain foods at the expense of others. As discussed in this abstract (Benton, 2004):
Children are more likely to eat in emotionally positive atmospheres. [...] Restricting access to particular foods increases rather than decreases preference. Forcing a child to eat a food will decrease the liking for that food.
Sounds like, if you are particularly concerned that she should drink milk, just act like it's a treat rather than a burden that she has to do, and that it's a treat you like to have as well. On the other hand, forcing her to drink milk may lead to her develop a real life-long aversion (Batsell et al, 2002):
Specifically, the most common type of forced consumption (76%) involved an authority figure (e.g. parent, teacher) forcingachild to consume a novel, disliked, or aversive food. In this authority figure scenario, respondents recalled the episode as involving interpersonal conflict and negative affect, and identified the most aversive aspects of this scenario as lack of control and feelings of helplessness. Furthermore, most respondents (72%) reported that they would not willingly eat the target food today.
So, making food part of any kind of disciplinary activity could backfire on you badly, unless that food is considered a reward. There's some suggestion that this is the origin of the 'sugar high' (Hoover and Milich, 1994):
In the experimental group, mothers were told their children had received a large dose of sugar, whereas in the control condition mothers were told their sons received a placebo; all children actually received the placebo (aspartame). Mothers in the sugar expectancy condition rated their children as significantly more hyperactive. Behavioral observations revealed these mothers exercised more control by maintaining physical closeness, as well as showing trends to criticize, look at, and talk to their sons more than did control mothers. For several variables, the expectancy effect was stronger for cognitively rigid mothers.
In essence, getting something 'forbidden' was so bad for the mothers that they became more controlling, while the kids themselves thought that it was awesome to get something they couldn't.
tl;dr: If milk suddenly becomes 'forbidden', then maybe she will start to think that it's awesome.