Hi A.,
I have a 21 mos. old daughter and just recently started going timeouts. I make her sit on the rug by the front door, we hardly ever use it so it's out of the traffic pattern of our home. When we are outside and she has to go to timeout, she sits by the back door on the outside mat. This has proven to be sufficient for us and very convenient. It surprised me how well she obeyed, she only tried to squirm out of the spot the first time and that was it. Like the others said, you have to be consistent, get down on their eye level, tell them why they're going to timeout and when they're done, get back on their level, recap the reason/what their appropriate action should have been and then give hugs. Also, I have found that if I warn her or even mention "sitting by the door" she'll go and put herself in timeout, while that is very convenient, I think the discipline needs to be a direct action from you each time, you have to get up and physically be involved in the process, otherwise they will start to get confused. We use the phrase, "not until you're a happy girl" a lot so that she can start to figure out how to control her emotions and it doesn't reflect on her self esteem like saying "are you going to be good?" or "you've been a bad girl" etc. I don't know if that part really makes much sense but I like reminding her to be happy rather than hording a lot of negatives over her. Good luck, 15mos might be a bit young for them to grasp the whole concept but it's definately worth a try.