Hi and welcome to BYC! I have been raising and showing competitive miniature dairy goats (specifically nigies) for over 9 years, and we treat all our goats like pets. Nigerian dwarves are my all-time favorite breed of dairy or any other goat, so I must encourage you to try them out.
It sounds like you want to keep them as pets and brush-eaters. They make exceptional pets, are comparatively gentle on fences, and are very gentle with humans unless they've been trained from a young age to "play butt". However, I can tell you that you would need a herd of over 20 Nigerians to do significant damage as far as clearing brush. Nigies do enjoy fresh spring & summer foliage, but will eat nothing but the tallest of canary grass and any trees/shrubs that they can reach. That is why I always try to get the word around that goats aren't replacement lawn-mowers. One of the biggest differences between goats and sheep: sheep "graze", goats "browse".
If you do end up milking your nigies, I think it would be a rewarding experience for you. Nigerian Dwarves have the highest milk fat percentage of all dairy breeds and the milk is said to be the least "goaty" in flavor.
Just one more thing; you should try out nigies if you Really want to and have the time and knowledge, but maybe wait a few years so that your kids will get more out of it. Also, they will be able to help you with the goat chores better. Goats won't just shove you out of the way... unless you are between them and tasties. So I would say the kids would be happier and more confident around the goats if they were a bit older.
Hope I didn't discourage you & blessings to you & your family,
Becky