>>> Is 3 nights in Carpathian too much? Should we increase 1 night in Kyiv?
I don’t think so, considering that your travel interests are focused on nature (mountains etc).
>>> Yalta and Odessa similar?
Not a bit.
Yalta is a small coastal town with not much to see in it (compared to Odessa), very quiet in the low season and extremely crowded in high (mid/end-summer). But it gives you a terrific base to the entire southern coast of Crimea with its ample historic sights and natural wonders; all very close and reachable by taxi/public transport. Also, there is no comparison in Ukraine to amazing Crimean nature, so I can not recommend you to give it a miss, considering your travel interests as you described them above.
Odessa is a larger port city, and a character in its own. It has lots of things to do and see in the city (Opera House shouldn’t be missed, if you like classics).
Mind though that I’m biased and just love Crimea ;)
Browse for the photos of both, perhaps it will help you to make up your mind? Start with those available on TA (look for Photos in the left-hand menu on respective pages tripadvisor.com/ShowForum-g313972-i7465-Crim… and tripadvisor.com/ShowForum-g295368-i5302-Odes… ).
Just some suggestions for you to consider:
(a) Should you decide to give Odessa a miss (for whatever reasoning), take a look at the city of Sevastopol in West Crimea with nearby Balaklava, Inkerman, Bakhchisaray http://tinyurl.com/dypn2xq and Cave Monastery of Chufut Kale http://en.wikipedia.org/wiki/%C3%87ufut_Qale It’ll be very easy to get there from Yalta.
(b) Should you decide to skip Crimea, consider adding one night to Lviv, so that you could visit its nearby castles. Say, in Olesko http://en.wikipedia.org/wiki/Olesko_Castle , Pidhirtsi es.wikipedia.org/wiki/Castillo_Pidhirtsi and Zolochiv http://en.wikipedia.org/wiki/Zolochiv_Castle This “Golden Shoe” is a minimum of what you can see; there are many others nearby tripadvisor.com/ShowTopic-g295377-i5799-k427… Then one more night can be added either to Kyiv, or to Carpathians.
>>> not too sure on how many days we should spend in each of these places..
Your current itinerary looks quite balanced to me if you want to quickly see the best of Ukraine.
But you are right, considering the distances and how slow Ukrainian trains are, you might, indeed, spend too much time on the road moving between Crimea, Odessa and Western Ukraine.