First hand experience in reroute. AB cxld DUS HAM. Offered train or car rental coupon. Refused to reroute on LH even thought they were operating because the agent said there is no interline agreement with LH.

Train coupon is two pages (carbon copy). Agent writes down your info (name/PNR/ticket number/route). You board DB train with this. You can also pay to reserve a specific seat on the train if you want (recommended if you are travelling with a large party or with kids). Train personnel will stamp both copies and keep page one. Just show your copy on subsequent train connections.