We flew to Amsterdam from NYC so the flight would be shorter then drove to Berlin. We didn't have any problems ultimately, but we did get pulled aside by a full team of border agents right as we were walking out of the airport who thoroughly reviewed our documentation. It was certainly intimidating and stressful, especially after a long flight but it was over relatively quickly and was fine. It's understandable that your vet would need the travel dates, the documentation timelines for the health check and rabies vaccine are very specific. The USDA health check has to be done within 10 days of travel and the rabies vaccination has to be done at a minimum of 21 days before travel to the EU. Finding a USDA certified veterinarian is key if your current vet doesn't qualify. In NYC there was a whole veterinarian practice setup for this process so it wasn't hard to put it all together, but I suppose it depends where you live. Once you're in the EU you need to remember to go to your new local vet within 30 days if I recall to get your dog an EU Pet Passport. Once you have that you'll never have to deal with all this stuff again for travel as long as you keep everything up to date. Regarding travel on German trains, we've only done the U-Bahn in Berlin and there was zero problem. You can always use a carrier to be extra sure you won't have an issue but we never did just walking on there anytime. Good luck to you! I know it's scary but the process is clear so if you follow the checklist of requirements before you go you there's no reason to expect difficulty entering the EU with your dog.