I agree that training, knowledge, and muscle memory are key to safety. However, The key words here are "As long as your 1911 safety functions correctly" firearms do malfunction and you have no idea whether the safety that worked fine 10mins ago is still functioning properly due to powers outside of your control. Granted this is a very small chance but having a child I want to have the extra safety and the extra retention.
I'll be honest, I do not rely on safeties. The majority of the time I carry a very old Colt 51 cartridge conversion, there are no safeties. I have carried a single action either revolver or semi auto most of my life. My first handgun was a 49 Colt clone pocket pistol(I still have it), no safeties, just cock and fire. So I carry my 1911 in the same fashion(condition 2), but most people carry condition 1 which is perfectly safe. If your gun is in working order I highly doubt it will have a dysfunction. The thumb safety from the factory is positive(does not come off without some force). That is not going to change unless you or someone else buggers with the gun. Leave it alone it is supposed to take some force to disengage it, if it does not, then send it back to be repaired. Otherwise relax, train, relax, train, do not ever touch the safety until you are on target and need your gun. You will be fine as long as you trust the safety to stay on and leave your fingers/thumb off of it while carrying. When you start your day VISUALLY make sure the safety is on before holstering, and to be repetitive past annoyance, keep your thumb off of it until you need it.
BTW keep your fingers/thumb off the safety until you need it, and are on target.
I'll get down off my pulpit now, and stop preaching.
PS two things about your children, they cannot get your gun while it is in a holster on your hip, or locked in a secure box/safe. But they should also be taught to not touch a gun, any gun, unless supervised by an adult.