Seems like this should be more fair all the way around. What we have with this isn't free trade.
I just wasn't aware of any major outstanding issue that required a "trade war" type scenario with these countries (EU/Canada/Mexico) now.
The issue with trade wars is that the tariffs that result can end up lasting far longer than one might expect, and from what I see most economists consider the overall impact negative. The 25 percent tariff on light trucks in the US for instance comes as a direct result of a minor "trade war" between West Germany and France on chickens from approx. 1961-1964. (https://en.wikipedia.org/wiki/Chicken_tax)
Generally speaking, if a tariff another nation imposes is bothersome, removing tariffs in a negotiated deal is what has tended to work over the last several decades. That 10 percent auto tariff was recently negotiated away in Japan, for instance, with Japan likewise removing some tariffs they applied on EU products. (http://europe.autonews.com/article/20171208/ANE/171209797/eu...)
In the case of China, where they are more prone to violating WTO rules, that approach might not work, and a more aggressive stance might be justified. But the EU, Mexico, and Canada? Not so sure there.
But I'm honestly not sure why his administration seems to also be targeting allies such as the EU, Canada, and Mexico. I'm sure there are "quibbles" with trade on trade with these countries, but my impression was there were no major problems there.
The other problem with Trump's tariffs IMHO is what you point out: there is a lack of coordination with allies, and a general chaotic nature.
Overall, uncertainty on this front probably isn't the best for business planning, given that the tariffs have more of a whiff of generic isolationism than punishing any misdeed.