13 Month Old Won't Drink Milk. Gone 3 Days with NOTHING to Drink per Dr. Help!

This is my first question posted here & I’m really hoping you mama’s can help! I apologive in advance how long this is, but I feel I need to fully explain my situation to get the best advice. My DD is 13 months old & we’re trying to switch to whole milk. Quick precursor: at 3 months old we discovered she was “sensitive” to dairy (not full-blown allergic, just sensitive), so she was on a hypoallergenic formula from then until 1 yr. At 9 months, Dr. suggested we start trying some dairy – yogurt, cheese, etc. She’s tolerated them fine, even likes them a lot, and has had no issues. Seems the dairy sensitivity was over (yeah). Ok, back to my issue today. My DD loves water & drinks it out of a sippy with meals, during playtime, etc. She won’t drink juice at all. About 3 weeks ago (just after her 1 yr. check-up) the Dr. recommended we cut to milk cold turkey (because she's stubborn - Dr.'s words) & offer her nothing but milk. Dr. said kids usually give-in at the end of the 1st day or 2 (max), and drink it up because they’re so thirsty. Well, not my daughter. 3 full days went by & she didn’t drink a drop – not from a bottle, sippy, even mixed with some formula on day 3 for the taste she was used to – just flat out refused! She’d look at her sippy, could tell it wasn’t water & would not even try what was in it. So, I called the Dr. back after 3 days & she said to go back to formula in bottles & water in sippy for a few days to get her drinking well again. Then try the transition method – ¾ formula, ¼ milk in bottle…then move to ½ & ½, then ¾ milk & ¼ formula, etc. This was working fine for about a week and a half & she was about to ½ & ½ mixture when all of a sudden she just stopped drinking from the bottles…she’d just push them away & want nothing to do with them. So for 3 days she only drank water from her sippy. I called the Dr. back again & she said we’re going to have to do the cold turkey thing again…and, yes, since DD held out for 3 days last time, it might take 5 to 7 days. She said to let her even get a little “dry” (slightly dehydrated) so she’ll be extremely thirsty & give-in & drink the milk. Does this seem too extreme? I’m freaked out to let her go that long with nothing to drink. I can’t give her water, as that is what she is holding out for & wants. As I mentioned, she won’t drink juice. So she literally gets offered milk in a sippy (since she won’t take a bottle anymore) and if she doesn’t drink it…that’s all I can try to give her. We’ve tried all different kinds of sippy cups…she won’t try most & pushes it away if you try to put it up to her mouth. Daycare made a game out of it getting the other kids involved and she lifted the cup to her mouth & got a little, but dribbled most of it down her chin & doesn’t swallow it. That was day 1 of this 2nd try at the cold turkey thing. 2nd day DD wasn’t playing that game anymore & drank nothing. We’re on the 3rd day & she’s still not drinking & pretty much not even trying anything you put in front of her. I know she’s not dehydrated yet; she’s getting fluid from foods she’s eating & still crying tears, peeing every 8 hours at least, etc. She is smart & obviously stubborn…and I’ve already seen her manipulate other situations with me. Is she really just THAT stubborn & manipulating the situation (which I know she understands already)? Or could there be some other explanation? She eats yogurt like it’s going out of style & it doesn’t bother her at all to digest. So I cannot imagine what little milk she’s actually gotten over the last several weeks makes her tummy upset, thus causing her not to want to drink it. I’m at a loss as to what to do. I plan on calling the Dr. again tomorrow to discuss a plan before the weekend, even though it will have only been 3 ½ days…but I just have this feeling she’s not going to budge. Did anyone out there have a similar problem??? Anyone I’ve talked to says they’ve never heard/seen a 1 yr. do this/hold out this long. What do I do? Ask the Dr. for vitamins & just give her water for now…then try milk again in a few months time? Wait DD out? I appreciate any advice.