I am sorry to see that your question morphed into the thread it did and realized that you really didn't get an answer to your monitor questions.
Some monitors do tolerate handling to some extant others do not. Some species of monitors are better than others at having individuals that will tolerate handling.
Generally speaking however monitors should really be considered a display animal instead of an animal to be handled and carried around the house, it stresses them out.
I kind of get the impression from your post that you may want a large lizard that can at times roam around your house as well. Once again monitors are a bad choice for this given that they tend to want to hide in holes and such in nature and will try to do likewise in your house where they will be even more stressed. If you look up some of my old posts on here I mention some instances years ago where I tried this with a large water monitor and I ended up ripping out a wall to get it out of where it went. I also mention a few other incidents in some posts as well, look them up.
I have found that green iguanas tend to be quite tame in captivity and can tolerate handling much better than most monitors they can also be allowed to wander in the house under close supervision for a while but once again should have a dedicated enclosure for your safety and theirs. They get plenty large for most people, they do however require a complex vegetarian diet not required by monitors. Bearded dragons get a decent size to them as well and are quite handleable by children which seems to be one of your concerns as well. You may want to consider one or the other or looking into some other species. On a good note about niles, while they tend to be aggressive they are as tough as nails and if you should decide to keep it as a display lizard it should do quite well for you if you give it the proper conditions.

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