Thanks for the advice! I appreciate it. I decided to nix Amsterdam to spend more time in other cities

If we left May 6th and came back June 6th ☺
Day 1 Travel to London
Day 2-4 London
Day 5 Afternoon train to Paris
Day 6-8 Paris
Day 9 Versailles
Day 10 Spend the day in Paris, Night train to Berlin
Day 11-13 Berlin
Day 14 Afternoon trip to Prague via Train
Day 16-17 Prague
Day 18 Spend the day in Prague, night train to Budapest
Day 19-21 Budapest
Day 22 Train to Vienna
Day 23 Spend the day in Vienna, sleeper train to Venice
Day 24-27 Venice (possible day trip to Florence?)
Day 28 Fly to Barcelona
Day 29-31 Barcelona
Day 32 Fly Home ☹