Unfortunately, the years do not add up as the Second Schleswig War took place in 1864, not 1870. However, there is a possible explanation that makes your ancestral story plausible. First, it is entirely possible that Vamdrup and the surrounding area were sacked or at least occupied by Prussian/Austrian troops during the Second Schleswig War, as they did advance as far as Kolding. So as far as that part of the story goes, it's a definite possibility and makes perfect sense.

Vamdrup, from what I can see on Google Maps, would've sat just on the border of either Denmark or Prussian occupied territories at the end of the war. It's possible that the demarcated border line settled on in the Treaty of Vienna may have actually split the town or at least cut part of the local community off from Denmark and made it Prussian territory. This ties into to the second part of the story because, if your ancestors were living in Prussian-controlled territory (or incredibly close to it), their eldest son could easily have been forcibly conscripted into the Prussian army in 1870 on the eve of or during the Franco-Prussian War, which started that same year. At the time, the Prussian army relied heavily on conscription, so that's definitely a reasonable thing to have happened.

So, my theory is this: Your ancestral story is two conflated tales. One tale is that of German soldiers sacking Vamdrup during the Second Schleswig War. The second tale is how the eldest son was forcibly conscripted into the Prussian military during the Franco-Prussian War. Over time, those two stories may very well have been conflated into one story about how German soldiers showed up and destroyed the town and kidnapped the eldest son. My alternative theory is that the Prussian soldiers showed up to forcibly conscript village residents and were not very nice about doing so, which eventually grew in telling to become the story you have here, but I think the other theory is far more likely and probably exactly what happened.

As for what happened to the son, I'm afraid I can't provide you with a lot of closure. Speculation on my part (not very historical of me, apologies): He probably died fighting or of some other malady before he reached fighting. Without knowing what happened to him after conscription, it's hard to say what unit he would've ended up in and where he would've fought (if he ever even reached the front). Regardless, tens of thousands of Prussian soldiers died or went missing during the conflict, and I am afraid he was probably among them. Three other alternatives (two depressing/one not) also present themselves. The first is that he did not die, but either remained in the military for long enough that when he returned home, his family had left for Australia and he was not able to track them down. That seems unlikely but is not impossible. The second is that he remained in the military and made a career out of it, but failed to contact his family ever again. Unlikely, but not impossible. The third (and happier) theory is that he found some nice woman somewhere during his time in the military, either in France or in what would soon be Germany, and when he mustered out of the Prussian military he went and found her and settled down and had a long, lovely life. Unlikely, but not impossible. Think what you like, I'm going to go to bed believing the third alternative is what happened.

I hope all that helps answer your question. In short, your ancestral story is entirely plausible and most likely happened.