Maybe a combination of the two?
You mention Germany -if you want to explore the Alpine area, think no further than a little town called Oberstdorf. there is a station there and inter-city trains terminate and start from there. If you look at booking a Gasthaus, or a ferienwohnung (self-catering holiday flat) some are part of a scheme whereby the cable cars and chair lifts are all free. There is a lovely swimming complex in Oberstdorf and a huge one in nearby Sonthofen. Your daughter would love the Rodelbahn (google it) at the Sollereck mountain. If you are really interested, then PM at some stage for further help. A truly idyllic place.