No not all births are traumatic. But who gives you a guarantee which kind yours will be before you invite your young children in? Even if they aren't traumatic, they are still intimate, messy and painful. Why exactly should a child see that?
I can't imagine what difference it makes what position you birth in. The baby comes out of the vagina. If someone saw you giving birth, they saw your vagina. Even if you were kneeling on the bed, that still means you were naked from the waist down and your bare behind was on display for your young son to see. If thats OK with you, great.
Its very well to say your son was at liberty to leave, but are young children really mature enough to process all that and make those decisions in the moment? By inviting him in, you effectively took that choice from him. If there was a waiting area available, why didn't you let him stay there while you were pushing? Why was it necessary for a young child to see you push his sibling out? What purpose can that possibly solve?
Irrespective of whether you spread your legs or not, you do realise one is naked in the shower? If your children see you in the shower, they see you naked. When your son is thirty, he will remember what his mother's boobs and ass look like and he will know that she trims her pubic hair. Is that healthy or even normal?!
Nudity may not always be sexual, I am quite aware of that. I just don't understand why everyone in your family must see you naked so that you can reinforce your belief that nudity is natural.
Lastly, my nephews were not in anyone's bedroom. Please point out where I said that? They found the magazine in the sitting room while we were all in the kitchen. Then the kids were invited up to their cousin's bedroom to play (as is the routine) and there we found all the boys reading the VS.