So your first concern about this differing from the Crimea situation bc Putin wants to annex all of Ukraine is based on a false premise (that's been perpetuated by Western media).

Ukraine has 24 oblasts (https://en.wikipedia.org/wiki/Oblasts_of_Ukraine), of which the territories currently under dispute account for only 2 small eastern ones that border Russia (Donetsk and Luhansk): https://en.wikipedia.org/wiki/Temporarily_occupied_territories_of_Ukraine#/media/File:Russo-Ukraine_Conflict_(2014-present).svg. These territories declared independence from Ukraine in 2014 along with Crimea (also shaded pink in the linked map but further south) and like I described above are majority pro-Russia (https://en.wikipedia.org/wiki/Novorossiya_(confederation)), ethnic russian, predominantly russian speaking, carry Russian passports and driver's licenses, etc. For all intents and purposes the Donbas region has already unofficially joined Russia.

When our media talks about Russia invading Ukraine, they make it sound as if Putin's goal is to swoop in American style and topple the government in Kyiv (like Libya, Iraq, etc). But the Ukrainian government itself hasn't supported that assessment (eg. https://www.politico.com/news/2022/01/28/ukrainian-president-downplays-imminent-invasion-00003219 ) and has cautioned the West against alarmism.

I think Putin wants to annex Donbas but is exploiting NATO's eastward expansion as pretext/justification for militarizing the shared border with Ukraine. This way, Russia is simultaneously prepared for any response it may provoke with its land grab (bc Putin knows circumstances have changed since he got away with annexing Crimea) and maximizing pressure/deterrence about NATO.

As for what the US should do differently, I don't know but I really don't think further escalating is the way - especially since NATO is unwilling to appease Putin's concerns about expansion. By egging him on, the US is accelerating a moment that Putin has been waiting his entire life for to bomb/humiliate/exact vengeance on the West. I doubt a diplomatic solution will be easy, especially since NATO can't really turn back the hands of time on its expansion. But the fire and fury talk is super irresponsible. I much prefer Obama's restraint in response to Crimea.


Also re: the other question you pose, about whether people in Ukraine want to be a part of Russia, I think Ukraine's recent political context is helpful:


* Ukraine's current pres Zelensky (https://en.wikipedia.org/wiki/Volodymyr_Zelenskyy) is young,chill, West- and EU-friendly, but has only been pres of Ukraine since 2019. He was elected on a platform emphasizing unity and rooting out corruption, and a big thing he's done is codify Ukraine's intent to join NATO into their constitution and initiate first steps.

* Before Zelensky, Ukraine was led 2014-2019 by a staunchly nationalist West- and EU-friendly oligarch named Poroshenko (https://en.wikipedia.org/wiki/Petro_Poroshenko) who was elected/installed as an independent and was a LOT more antagonistic towards Donbas separatists (calling them terrorists, pirates, etc). A big thing that he did was sign the Ukraine–European Union Association Agreement which was viewed as a first step towards Ukraine joining the EU.

*Before Poroshenko, and preceding Ukraine's 2014 regime change/"revolution" (in quotation marks bc some believe the Ukraine revolution was not organic but rather a West-backed regime-change op to install a more West/EU/NATO-friendly Head of State), Ukraine was led 2010-2014 by long time Prime Minister-turned-President Yanukovych (https://en.wikipedia.org/wiki/Viktor_Yanukovych) who was from the Donbas region, ethnic russian, and somewhat neutral in the sense that he was slightly nationalist but also pro-Russia in policy orientation (eg. a big thing he resisted was signing the Ukraine–European Union Association Agreement, and he also sought to align Ukraine more with Russia instead of NATO). Yanukovych was deposed during Ukraine's controversial regime change/"revolution."


I think this electoral history is important, bc the fact that a Russian-Ukranian pres (Yanukovych) from the Donbas region was not only democratically elected by the people of Ukraine but appointed Prime Minister/Head of Parliament 3 times by multiple presidents speaks to the size and influence of the ethnic Russian/pro-Russian population there. Then, after Yanukovych was deposed during Ukraine's regime change/"revolution", the subsequent pres (Poroshenko) was kind of like a Trump (even employing Paul Manafort as a consultant according to his wiki lol) - very brash and nationalist and oversaw great instability due to his antagonism of Russia and Donbas separatists. Ukrainians then chose not to re-elect Poroshenko and instead elected current pres Zelensky, who ran as a progressive unifier (so I'm guessing still EU friendly but no so nationalist that he alienated Ukraine's ethnic Russian and/or anti-EU population). And as we've seen in this current crisis, Zelensky is much more peace-oriented than his predecessor (even trying to get the West to cool down our rhetoric https://www.cnn.com/2022/01/27/politics/biden-zelensky-call/index.html). So from all of this, my take is that the people of Ukraine want peace most of all, and don't seem to want to go to war over issues like EU membership, NATO membership, Russian ethnicity or affinity, etc. The Ukrainians who are die-hards about these issues seem to be fringe minorities, with the most die-hard Pro-Russians going as far as forming separatist Republics, declaring independence from Ukraine, and seeking closer alignment with Russia - which has contributed to the current crisis.