In response to your questions. As you most likely already know, if you are a resident of Taiwan who is male, and not handicapped or mentally retarded, then you have to serve in the military. So if you are a male that is not over 36 years old, not served in the military and has a Hukou in Taiwan and enter the island with an ROC passport... then good luck trying to leave the country! What most of my friends do is enter with their US passports, of which only has a 90-day visa-exempt period. If you are a female, I don't think it is as complicated.
There are also two types of ROC passports: ones that are issued to people born in Taiwan and another type issued to children of Taiwanese nationals that were born overseas. The latter type of passport is called a "僑民護照", it is essentially the same as the former one except that it does not have an ID number. This is the type of passport your kids can obtain. You can apply for them at any of the Taiwanese embassies (or visa-issuing offices). With this passport, you can enter Taiwan, but you will need to get a "permission" before hand and there are also restrictions as to how long you can stay. This type of passport also does not have the visa-exempt features that the regular passports do. This passport will give your kids the ability to obtain residency in TW in the future should they chose to, they just have to live in TW for 1 year to obtain their ID card. There is always a catch though, once you obtain your ID card, if you are male, then you have to serve. I am in this exact situation. I'll be starting my new job in TW but I am going to have to enter with my non-TW passport, then work for a year when which I will be over 36, and then re-enter with my "僑民" passport to apply for my ID card to become a resident. The current conscription age limit is Dec. 31st of the 36th year you were born. So on Jan. 1st, 2016, everyone who was born in 1979 no longer need to serve. This "law" is very weird since it is unfair to anyone who was born in the early months of the year, but it is what it is. Do keep in mind that this law is ever changing and it may just be abolished by the time your son reaches 20.