I'm supriced they did not teach them how to tune the instruments. It does no good to practice with out of tune string instrument. How will she know where to place her fingers?
My 8 year old plays violin and when she started I had a electronic tuner so I could tune the violin before she practiced. It will not be perfectly tuned that way but I never learned how to do it with my ear. Luckily DD has perfect pitch so I do not need to tune it anymore. You should get a tuner for her.
If the teacher had to tune it twice in one day, then it is likely either the strings need to be replaced or there is damage to the fine tuners or the pegs. Of course, it is possible that your DD knock it out of tune or the cello experienced a temperature/humidity change during the day. Either way, you should have the rental company check the instrument and repair as necessary.
Do cellos really stay in tune that well? DD often needs to adjust her violin tuning in the middle of the practice or lesson and so does her teacher.
