Hello all.
I am the mother of two young children and have been a proponent of early learning since before I had my children. I am also one of the creators of a DVD entitled Trebellina which teaches young children (birth to age 4) about music, specifically, how to read music, pitch, and instrument names and sounds.
I am going to make my debut in the Forum posting an answer to this question.
My husband and I both play piano and we own a piano so that is the instrument that we decided to teach our children.
While a true piano is not scaled to the child as a violin can be, a child can have great success making beautiful sounds come from the piano right from the start. That is much more difficult with a violin. [While there are child-sized pianos but I find they sound cheap and tinny as do many small violins.] The musical range offered by the piano is far greater than the violin and all but the very youngest babies can depress the keys. While a piano itself can be a costly and space-consuming investment, a high quality keyboard is not. We bought on on the Costco website for a very reasonable price.
While we can debate the merits of piano vs. violin for the young child, I hope we can all agree on the value of music for brain development and that teaching our children any instrument will be of great value to them.