Something to think about is that 4 and 12 are vastly different ages. At 4, she may be too young for an instrument, but she could get into singing and just experiencing music. I've been around quite a few small kids learning music, through the music programs that my own kids went through. I've observed that little kids seem to "get" melody before they get harmony. It may seem counter-intuitive to teach your daughter simple melodies before chords, but it might be less frustrating and hold her attention better. You can sing melodies, meaning that you can memorize them before you play them.My daughter says she wants to play guitar. She'll be 4 in a couple of weeks. More than a year ago, I was looking at small-scale guitars asking her which one she would like to play. She said "I don't want to play guitar. I want to play bass, like daddy." Naturally, I lit up. Since then, she has primarily shown interest in guitar, and my Ibanez 540S is her favorite. She calls it her guitar. Sometimes I set it in her lap and she goes through it string by string. With a bass, she usually just beats on the strings in the upper register. I've started to introduce her to fretting and whatnot. Her fingers aren't strong enough yet. Anyway, there will be a kid-sized guitar in her future, maybe Xmas/birthday next year. But, I'm not going to get her something that I want. I want her to be excited, not viewing it as a chore. She likes the Daisy Butterfly and a pink Strat-like guitar. I guess we'll see what she likes next year.
No one had to force me to play. I saved money and bought my first bass myself. I have always been heavily into music, so I never needed any kind of nudging. Is your son really into music? If not, it will be a chore to him. I play because I love to play, and it brings me great joy. Why do you play? Did someone force you to when you were a kid? Advice to impel a 12 year old boy into playing: Chicks love good musicians. Start now, and you'll be good by high school.
Whatever she enjoys and is interested in, is preferable to what we adults might think is the right thing relative to our own musical ambitions. Don't recoil in horror if she likes classical music more than pop. Been there. There are kids guitar methods that could provide some guidance as to what things are easy for kids to learn first. In the Suzuki violin method, kids start with extremely simple melodies that they learn by ear, and there's a certain inherent reward to advancing through the books. People have worked on methods for teaching music to kids, that work. You don't have to re-invent the wheel.
I always mention that it's a judgment call, every kid is different, every family is different.
Did someone force me when I was a kid? At the age when I learned music, it's nearly impossible for kids to pursue any interest without some push. My parents must have known that I was interested in music. I got to choose an instrument, but my choices were not unlimited. I tried piano for a while, then the recorder, then flute, and eventually settled on cello in 4th grade.
I think it's pretty commonplace for kids to be genuinely interested in something, yet lack the attention span and self discipline to make the effort needed to support their interest. They're kids. Even if they really want to learn music, they will still resist and procrastinate when it's time to practice. You may go through periods when you have to force the issue on practicing every day. Do you persevere because you know that deep down they're interested in music, or do you conclude that they're not interested and give up? Welcome to parenting. There's no right answer.
I think it helps to have a regular practice schedule, the earlier the better. Half an hour before bedtime is not a good idea.
Age 12 is different. Now they're interested in what their friends think, and what's cool. They are also no longer patient with massively delayed gratification. The attraction of instruments like guitar and bass is that you can make coherent music, and function in a band, almost instantly.
A word of caution is that you're never guaranteed that your kids will inherit your passion for music, and you have to be emotionally prepared in case they don't.