I was 10 when I started to play the violin, and I focussed on it completely for about 3 years before beginning keyboard lessons at which point my violin playing improved tremendously. In terms of time management, it wasn't too hard to fit in the practice for 2 instruments. I then started piano lessons as well, but after 6 months gave up keyboard lessons as I couldn't give all 3 the dedication each of them they required. A year or so ago I decided it was time just to focus on violin, and so gave up piano lessons. (Music wasn't my only interest, I also did linedancing, stage acting, and countless extra-curricular things at school.)
What I'm trying (but failing somewhat!) to say is that perhaps your daughter should be allowed to give it a go. If things become too much for her at some point she could always stop for a while and perhaps come back to the cello/violin once she had more time. I've recently started to teach myself the piano and viola and have found that time isn't always so much of an issue now, although at times I have to make myself just concentrate on violin for a month or so, depending on the amount of coursework/exams I have.
My mum used to nag me to practice too, and yes, there were tears on occasion, but in 4/5 years I think your daughter will see the benefits. Hope this helped even a tiny bit!