There's no reason that wouldn't work from a durability standpoint. In fact, having both sides painted will decrease the possibility of warping when it is rainy or humid. Just check to see what the appearance looks like with a couple of boards in place, since siding like that has an a slightly asymmetrical cross-section. Also your approach has the advantage of not being exposed to lead dust, which would arise from sanding through layers of what is probably old, lead-containing paint.

Thank you all for the excellent feedback regarding the siding.. I am definitely going to replace all the landscaping.. Do you have any suggestions for what it should replace it.. Perhaps visuals.. I've tried finding free software that I can upload my picture and play with different ideas but so far no luck

Thank you all for your comments. I am still so torn because the trim on the siding is rotting away, especially on the back of the house that faces north. Granted, this wood is probably 25-30 years old... I am concerned that it will begin to rot again, when new wood is replaced. Our window sills are rotted and even windows are rotted. I assume this is from rain and maybe it can't dry out enough on the sides because the houses are close together? I just hate to waste a huge chunk of money on painting/staining the existing siding and have it all go to waste. It is going to be $18k to do the hazmat removal of the lead peeling paint, replace rotted wood and then put new wood siding on the addition. It's not like this is a $5000 job... Another concern is that I just found out a lot of moisture gets into the walls and seeps out of the house? Is this true? From cooking and showering? So this can cause the paint to fail prematurely if there is no vapor barrier, which there wouldn't be, since the cedar is original to the house in 1918. I also have concerns about going over cedar with vinyl for the same reason. I am concerned that mold could build up under the new vapor barrier that they would put up... I remember one siding company said it is a bad idea to not remove the old siding and this may have been why. We have had issues with mold in various places like under the front porch, but once proper ventilation was installed, it went away. I just don't want to have everything sealed up to the point that no water vapor can escape and is encapsulated in between the layers of siding, causing mold growth. I'm probably over thinking it, but we are stuck in which ever direction we choose, and neither is "cheap".

Agree - depends on what your vision of natural cedar looks like.