It is great to teach piano first because it trains the ear. You press A, you hear A. Hard to get the right note on the violin.
In fact, you will see the piano accompanist help the early violinist tune because they don't know what A or C sounds like.
We were asked by the music school to start Dd before she was 3.5 and we said no. But then they pushed again when we started group piano lessons so we started when she turned 4. As she progressed fairly rapidly, it got to be a problem on pieces because she just didn't have the spread. More and more, pieces had to be adjusted for her span.
She did Russian method. I am not sure what it is, having learned a luke warm version of Royal conservatory growing up. She would just get pieces, though get Czerny studies for technical exercises. We are actually switching this year due to stuff going on and trying a Chinese student doing her Masters at Juilliard. She had a Chinese instructor in China, then a French one and came here at 14 and went to preJuilliard for high school. She met with DD and understood the boredom factor for a 7 year old and the Russian method and branching out.
A friend yesterday mentioned her kids go to Mannes music school which is conservatory method and she liked it.
I think it all boils down to the teacher. Finding a really good teacher is hard. One that gets your kid and making it work for them. Practicing is never fun.
DD can sit at the piano composing for 20-30 minutes. But to perfect a piece for the same amount of time, is like asking for her to walk on hot coals.
