My daughter is learning a cello piece which has a number of trills in it which last for a whole bar. However, rather than writing them as a semibreve, they are written as two minims. Is this just to indicate that she should change bows in the middle with no noticeable gap or should the audience have the impression that they are two separate trills?

I would try for a very smooth bow change so that it is hardly noticeable to the audiance.

It's hard to say without seeing the context - it could just as easily be intended to indicate either a subtle bow change or a clear articulation.

If this is any help, it's a sonata by B. Romberg (so I think late classical). The first of the two trills has an appoggiatura indicated, the second has the ending indicated (I have been doing too much music in French and I can't remember what the proper English term is but what I mean is (B)-A-B-A-B-A-B-A etc. (G-A) the trill being on the A and the notes in brackets the appoggiatura and the ending if that makes any sense).