I'm not sure how old your kids are, but we flew A LOT when my daughter was pretty little - like between 3 and 7. Until she got pretty comfortable, we would "practice" going through the security checkpoint. So she would unpack a backpack of her stuff onto a sheet that I then pulled through the hallway doorway. Then she would walk through the doorway really slow and quiet-like. Every once in a while I would have it "beep" and we would have to do it over.
I would say to practice for the body scanner you have her stand in the shower and hold her arms straight up for however long it takes (not sure on timing).
Also - for the pat down - you can practice with her. They don't actually TOUCH any private areas but they will go up right to the area.
I know there was that case of that 3 year old freaking out last week, but the whole time I flew (which was even right after 9/11) when my daughter was little (in and out of airports all over the US) TSA was generally pretty considerate with kids - although there are always exceptions I guess. Mostly I would get your child prepared to follow their directions without you right next to him/her and to go slow - when kids run through the metal detector it sets it off.
TSA will definitely take their lead from you. They are humans after all- If you are calm and your kid is calm TSA will be calm - generally.
Good luck and have fun wherever you are traveling!