Translation:We have a big dog that, however, no one fears.
I would say 'we have a big dog that, however, no one fears.'
The answer that the program keeps suggesting has 'whom' instead of 'that', which doesn't make sense to me. 'Whom' is generally reserved for people and not animals.
I also think that in general 'that' is preferable to 'which' in this context.
I think the missing "that" was just an ommission. I also changed the main translation.