I wouldn't worry aobut it. As long as he is nursing at least once a day he is getting all the fat and calories he needs, the milk he needs. Just keep offering. we aren't big milk drinkers here, my boys have cereal for breakfast and a small glass with dinner, thats it.
As long as he is still nursing, having cheese, yogurt, other dairy, just keep offering the milk, he'll drink it eventually. Make it a meal thing, milk with meals and water the rest of hte day. Don't stress about it, he'll be fine!
**edited to add** If your son eats greens and veggies, then he is getting all the calcium he needs. As for the healthy fats, flaxseed can be added to anything to add good fats, and most kids LOVE avocado, so push that too. Soy milk isn't all that healthy, look it up online, it has lots of hormones and its so overprocessed that its like sugar water with hormones in it. Almond milk is a good alternative for a dairy drink. We drink that alot here.
And he wont nurse until he is 18, the average weaning age worldwide is 3-4, and that includes the US whos average weaning age is 4 months, or not breastfed at all. Almost every toher country breastfeeds thier child until 2 or longer. Just let him set the pace, its not good for you or him to cut off nursing cold turkey, that nurse gave you very bad advice, I would disregard it if I were you. ITs not a power struggle, he is 13 months old for goodness sakes, he's not fighting your or being naughty on purpose! My youngest jsut weaned at 17 months with little help from me. I cut out his daytime nursing (before nap) at 13 months and he nursed morning and night until he was 15 months old, and then stopped in the morning by himself, and then kept the bedtime one until 17 months. It'll happen, cutting out the daytime ones isa good way to start but keep ti slow, one nursing at a time, and cut it out and wait a week or two before cutting out another one.
Good luck and remember that a healthy balanced diet is way more important that pushing cows milk, and breastmilk is the most important drink for your little guy!