I only played xylophone :-) as a child and from very early on felt that the lack of ability to play a musical instrument (in my case I was thinking piano)was somehow making me less of a full person, if you get what I mean.
DS started taking Suzuki violin at 3.5 at his own insistance (long story). I was taking lessons with him an practiced with him daily. DD was dragging my big, full size violin and constantly taking it out of tune, so she got her own little violin for her second birthday and I started playing with her at home (basically open strings, when older brother was practicing) and she also started formal lessons around 3.5 years of age.
It is a huge time commitement on the parent side, HUGE, but practice is quite easy and short when kids are little. It is more of a "play" for them. And rewards are cheap when your kids are young. My kids never had any "major" problemswith practice, that is refusing it, till DS hit middle school, but the attitide at the house is that he has invested so much time in this already and he is so good, that it would be very foolish and unwise to quit. See, problems generally start when thir lives become more busy and they become more profficient on their instruments and therefore have to practice more/longer. DS13 and DD11 practice 70 minutes every day at this point during school year. At summer it is different, for example, DS does not practice at all for a month due to other commitements and DD practices 2 to 3 hours each day.
I do not think that you can overschedule your child with an instrument at the age of 4. You will have to make choices, but the time commitement for the next few years will be minimal.
Both my kids also play non suzuki piano, started at 8 and 6 respectively.
