Sounds like a great trip. Time wise, it seems like you have nearly a week in each of the countries you listed in eastern Europe, and 5 or 6 days in the cities in western Europe. This is quite a comfortable pace if you stick with this schedule. In Eastern Europe you do seem to have more destinations listed, so you won't have as much time in each place, but not every stop will require three or four days, so you can just change things around as you travel - stay longer in places you love, less time in those with less appeal.
We spent about 2 1/2 days in Athens (which was plenty for us), and two days in Bratislava covered most of the basics, while Budapest, Prague, and Krakow still held plenty of secrets after 4 - 6 days. Gdansk is one of my favourite cities, in three days you can see most everything, but it is nice to relax a bit if you can. Warsaw is not my favourite city - on our last trip to Poland we didn't even bother with it, though you have to see it at least once. I think I spent two days there the first time I went to Poland, which was plenty for me (though to be fair, things have probably changed a lot in 15 years!) The museum showing the destruction of the Old Town after WWII is a must, though.
In Greece we spent 4 days in Nafplio, which is a good base for daytrips to other places in the Peloponnese. We went in March, and found the weather to be warmish though not hot - in the 10-20 C range. It was a pleasant change from winter in Lithuania, but not exactly summery. Another issue we found there was that a lot of accommodations were seasonal, opening on April 1, and that the transportation schedules change (and some links are completely closed) in winter/early spring, so we didn't have as many options for accommodations and travel as we'd have liked. We did enjoy what we saw, there's certainly plenty on "mainland" Greece to experience, it just wasn't the more typical Greek island hopping experience many do.
Weather wise, you're probably wise to start in Greece/Turkey and work your way north, February in Poland is not the prettiest... On my first trip, I went in April, and one day was walking under a cherry tree in full bloom, then a wind came up and I noticed snowflakes falling amongst the petals. The second time we went in July/August, which was gorgeous in Poland (even rainy in Krakow), but HOT in Budapest. You'll definitely need a warm sweater, waterproof coat and waterproof shoes, wool socks and a hat on your travels in Feb/Mar, at least.
But the advantages of going in the winter/spring are worth the extra gear, by far. Check the dates of Easter, and try to book your accommodation for the week either side early - most countries have a two-week Easter break, and it's a very popular time for family travel (and many families stay in hostels). Also, and infinitely worse, many schools use that period for their field trips, and you get whole packs of young teenagers staying in the hostels, with minimal supervision. Being a family ourselves, we don't tend to mind the family groups, but the school groups can get pretty rowdy! It's a good idea to book in advance, just to be sure to get a space. Or, try to pick somewhere a little less touristy for that particular week (you might opt to stay in a suburb and take the train in to *big city in question* that week.) Or splurge on a budget hotel, like Etap, and revel in the luxury of a private bathroom. Course, that's where families like ours will be, but at least you can lock your door...
Good luck with the planning!