But yes, your entry calms me down a little although I still suspect it might be more about you being a great teacher (which I very much doubt that I am for my DS - and one should not doubt...!) and your sons being rather exceptional...
Mayamama, everyone doubts and we all have bad days. This morning DS2 seems to have forgotten every bit of maths he has ever known. 4 years ago when I was here with DS1 I'd have felt like a complete failure. I now have enough experience under my belt to know in all likelihood he will be fine tomorrow.
Children learn in fits and starts, you can go months without seeing any noticeable advance and you feel a complete failure. Then suddenly it is like a switch, something clicks and they're flying and you are running in their wake wondering why you ever doubted. With my two I can see a definite link between physical growth and mental growth - our slack periods when we don't seem to make any progression tend to correlate with physical growth spurts.
I'm not a great teacher, I lack patience and energy all too often. And in my opinion every child is exceptional, it is why we home educate so we can let them be exceptional in own particular way. What I do have though is experience, both personal and through sharing and discussing with others. I now have the faith to know that bad days are exactly that and they pass, even when they seem to drag on (many home eders seem to struggle after Christmas for example).
I'll be honest and say working and home educating is difficult, even when your work is completely flexible, I am often up at 5am to grab a couple of hours head start on the day and can still be working at 11pm. If possible I sit alongside my son with something that I can easily look up from if he needs help while he works. I make use of computer based stuff such as Reading Eggs and Education City where I sit near him to help if needed and get on with bits of work. Fitting in trips and outings requires juggling but is worth it.
I am mortified thinking I will fail my DS (5.5) because I do not know whether I can deliver At this age it is pointless to worry about what will happen when he is 18 and looking at University/work there are too many variables between now and then. The issue is NOW, what is the best thing for now? I do not know why you are considering home education but to me the most important things at 5yo are that they are happy, secure and confident - plenty of time for academics when you've got those three sorted. If you take him out you are not burning your bridges, schools will always be there for him to go back to if wanted/needed. Neither is HE the only answer - moving school, flexi-schooling (temporary or longer term) can be worth considering.