1. First of all, they are less expensive than an acoustic version. Now, why would you want to go cheaper on this kind of investment? Well, you know yourself and your kids better than anyone.
Are piano lessons or interest in music just a passing fancy? You just want something to play around on to see if you like it and if, like a lot of other hobbies, it starts collecting dust, you're not out a bunch of cash.
Now, this is not to say that you can't spend a lot of money on a digital piano. There are some that are quite pricey, but compared to an acoustic, they are a bargain.
2. This kind of instrument doesn't take up a lot of space. Some people buy acoustics as an instrument plus as a piece of furniture. You don't have any space to spare for either.
Unlike an acoustic, this kind takes up very little space and it is portable. You can pack it up and put it in the closet while you aren't using it. You can also get one that looks like an acoustic one if you want.
3. You like to mix it up with sound and pitch and only a digital will let you truly experiment. You can make it sound like an acoustic or give a very digital, techno sound. If you don't have time to worry about the regular maintenance of acoustics, a digital is also a good choice.
Unlike acoustics, you don't have to worry about regular tuning, rewiring or re-felting the hammers. Everything is electronic so, you just need an electronic expert if you need repair work. Also, maintenance for an acoustic can be expensive because you do to have to follow a regular schedule if you want to keep the instrument in good working order for years to come.
5. If you are self-conscious about your talent, you can plug headphones into your digital piano and practice in privacy.
6. If you really like what you've produced, you can record your masterpiece and download it to your computer. There is no need for additional recording equipment. They also have their own amps and speakers.
If you would rather have a digital piano, for whatever reason, go for it. While acoustics can be elegant and produce beautiful music, sometimes it just isn't realistic to spend that kind of money. If you go with a digital and you or the kids stick with the lessons and decide they really love playing, then think about investing in an acoustic.
If space is your problem, an upright might still fit. If the lessons don't work out, well… your wallet may not that feel lighter after making the purchase. Music is open to you - rock it out or reproduce the classics with a digital piano.