can we do this by train in one day?
It's between 11 and 18 hours by train. So technically you can do it but it would be quite a stressful day as all train connections include 3-5 changes. Do Zermatt do Lake of Constance in one day and then Lindau to Rothenburg on the next day. Less stressful, more excitement and enjoyment.
Do you mean Rothenburg, Switzerland or Germany?