T.W.
Everything you mentioned sounds very familiar to me, except for the second child. My son is 22 months, he does get time outs when appropriate. My pediatrician told us to start around 18 months, one minute per year of their life. Sometimes he cries through the entire time out, and sometimes he doesn't, sometimes he tries to get up, but mostly he doesn't. If he does something wrong, we'll let him know and he'll get 3 chances unless it's something really bad like smacking me in the face. If that happens he goes right into a time out! After the second warning we tell him that he's going to get a time out if he does it again, usually he won't do it again (but that's after a couple months of time outs). If you are going to try time outs, you have to do it the second they do something wrong or they won't remember.
When putting your child in a time out, make sure you are telling her why she is getting a time out and stress that they can't do that. She may try to get up the first couple times, just let her know that she's on a time out and she has to stay there, keep putting her back in that spot. Let her sit there for a minute to a minute and a half, and then go to her and tell her it's ok but remind her why she was put in a time out. It's not hurting her, and she'll start to understand if you are consistent. Like I said, we have been doing this since my son was 18 months.