Not sure why you would go through Moscow. Sort of out of the way. Maybe you are getting a great deal on Aeroflot? But will make for a long trip and the Domodedovo or Sheremetyevo airports are not particularly memorable (or efficient). From Berlin I guess you might go into Vnukovo which I know nothing about. Still, like I said, wrong way / long way; to Slovakia. .
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Your bags will go direct through to your final destination on the trip over. You should only have to re-check when arriving back in the US. You will have to go through passport control when arriving in the EU but that doesn't take terribly long. I travel to the region about 3 times a year and have been through a great number of the airports and I feel very comfortable with a 2 hour layover, more to compensate for late arrivals than anything else. With a kid you might want to lean more for 2.5 hours just to be sure everything goes smooth or if you are flying Aeroflot.. Remember on the transatlantic flight if the plane is 10% late that equates to nearly an hour.
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ON the way back if you allow 2.5 hours to clear passport control and recheck your bags in the US that should suffice. OR, apply to Global Entry program and you can do it with a much shorter connection when entering the US.
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I use locks but I always wonder how many people have keys to those TSA locks. Its about all you can do and hope for the best. You might also arrange to arrive 2 days prior to when he needs the sticks just in case they get lost. lost bags are generally found on the next flight. Also check in early in the US to give TSA plenty of time to rip through your bag and look for G-d knows what; and still have it on the plane on time.
Slovakia is one of my favorite places, enjoy it and do a little sight seeing.
James
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Where is the camp in Slovakia?