Can someone please tell me which buttercream is the most stable? When I say stable I mean which one is the strongest as far as holding up under fondant or for fondant details to be put on?? I used Sharon's SugarShack recipe and while it crusts well, I still have trouble smoothing it. Furthermore, for some reason, it doesn't keep it's "whipped" feel and ends up kinda like silk and it's hard for me to put it on the sides of cakes. It keeps running down the sides & ends up on my board. 

Why don’t you give a try to “2 of everything “ recipe found in the recipe section of this site?  I use it for all my cakes   It can be made to crust or not   It is silky smooth so it’s easy to smooth on cakes   

My go to buttercream is "Buttercream Dream" with Watkins clear vanilla: https://www.cakecentral.com/recipe/2123/buttercream-dream

I find that it smooths and pipes really well. I attach fondant & edible paper decorations without issue. I don't cover cakes with fondant, but there are positive reviews from those who do. The top tier of this pikachu cake is  smoothed buttercream dream with fondant attached (bottom tier is just a dummy). The waves on the smash cake in the background are piped buttercream dream.