Oh dear, the poor dog, it could get run over, eat poison/discarded bones/other, or be kidnapped (dognapped?). Rotties are lovely dogs – Daily Mail notwithstanding.
I understand your and your wife’s concern re the rabbit and your expectations of privacy/sole occupation in your garden. Involving the Council is certainly tempting.
However, a number of stray dogs are put to sleep – arguably no bad thing – but perhaps you could find a Rotweiler Owners’ Site/Club or something on the internet and have a word with them? They may (or may not) intercede on your (anonymous) behalf… or even dognap the dog themselves?