I would also agree that it would be better to just send off for a British passport for your children. Have a look on
www.britainusa.com for details on how to go about it. My daughter was also born in the US to me, a USC and my husband, UKC. We applied for a US passport when she was just an infant, and now that we're moving to the UK, I applied for a UK passport for her as well. The process was simple, and it took about three weeks to get the passport back in the mail.
If your 5 year old enters the UK on their UK passport, I guess it wouldn't really matter if your child departs before you do.