Yes, the butter's yellow would be responsible for the orange... But that's the problem with all (or at least most) buttercreams...
The whitest one I know would be the Mousseline Buttercream by Rose Levy Beranbaum... because it uses only egg white, and not the egg yolk, so the only yellow comes from the butter... If you substitute the butter with Crisco white shortening the flavour, of course, won't be as good... but if you want to stick with buttercream, you can check this one out... https://youtu.be/SIRk8NKWa-k?si=QAeK4wnTA8aFvDed
A friend from Australia made a red car cake for her boy, and the red was definitely red enough... as far as food is concerned... She used a Marshmallow Fondant, which she said was much easier to make than regular fondant... and also much less sweet... And she did make flower cupcakes and a host of other pretty things with the MMF...
I found this method on youtube, and it sure looks easy enough... nothing worth paying a thousand bucks to learn from some class... You can try it out just for fun, if not for a birthday...
All you need is a bag of marshmallow, a bag of icing suger, and some Crisco shorteining... all of which can be purchased in CitySuper, I believe... so no need to hunt down those little baking stores / schools... Their prices vary a lot anyway... so much so that I keep an Excel file on what the 2 nearest stores charge for my commonly needed ingredients...
One point to recommend, though, is that you should add the colouring in after the marshmallows melted, before kneading in all that icing sugar... It will be much easier to get the colour evenly distributed than if you add if in the next stage...
Also, do bear in mind bus-red is a dark colour, and all the fondants are white-based... so it will take a lot more colouring to get to your red, after you get past the pastel stage...
Good luck with your next cake !! And have fun !!