I actually take a bus 2 1/2 hours so I can avoid connecting with my kids. Sooooo much easier. Being on the plane overnight and then having to get off, change gates and get on another plane was really grim. The bus is better because we can sleep right away (no having to check-in, board, etc.)
As a Flight Attendant and among the expat community here, I have seen way too many connection horror stories to promote this. If you still want to connect (and by all means, if it saves you money, do it!) but avoid it in winter. I got stuck in Chicago overnight once in a snowstorm (SFO-BOS). It was before I flew for a living.
With 11 1/2 hours in the air, I don't want to add any extra time to that. Once, we had to stop in Iceland and it made the trip so much longer (and really, really confusing for my then 3 year old who kept asking where her grandparents were and why we weren't getting off). Another time, I had to connect through the East Coast and we arrived 8 hours later!
Stopping to let the children run around is not worth it IMHO. We were running to our next gate so there was no chance to eat or do anything else. Our incoming was delayed and we barely made it. It was stressful.
For those of you who try to avoid baggage charges by bringing everything on board, be aware that it wont make you popular with the crew. When you pack, be sure to separate the things you need for your flight vs. the things you're just bringing on board. That way, if a F/A or agent tells you that you have too much stuff, you can easily gate-check one of your bags without realizing you have things you need in it and it's gone. Also, you can stow that bag wherever you can and just keep the one with you that you will use.
BTW, you don't have to bring flight manuals, flash lights and all the extra things that the F/A's are required to have with them so comparing your amount of stuff to theirs' isn't really valid.
About the seat belt sign... If you are on the flight and your little one needs the restroom, get up and use it. I'm not talking about on landing or take-off or if it's really, really bumpy but some pilots just love keeping that light on :/ I flew coast-to-coast on a rival airline once and darned if it wasn't on the WHOLE TIME! It was hardly bumpy at any time! I was thinking "What's up with this?"
If you get up, you get up at your own risk. So if you bump your head while in the lav, you can't sue the airline. You were warned.
I personally, would rather take the minimal risk of being injured vs. my toddler having an accident. The crew has to tell you to take your seat or remind you that the seat belt sign is on. Tell them "I know I'm up at my own risk" or whatever. Be nice and let them know that you are in a desperate situation.
If you're not big into rule-breaking (bravo!) you can try negotiating. Ask them when it will be turned off. I've called the cockpit with a "That sign has been on for ages and we have some bursting bladders back here in economy" pitch and it's worked. Also "Passengers would like to take care of their needs. Any chance of turning it off anytime soon? What should I tell them?" Hopefully, the FA's are sick of it too!
I used to say "I have to keep reminding you of the seat belt sign!" as people would dive into the restrooms. I wasn't going to accost them and force them back into their seats. So do what you or your child needs to do.