As Sadsmile said, products labeled non-dairy are not TRULY non-dairy. This includes non-dairy coffee creamer. This has an ingredient called casein, which is a milk protein. I am not technically 'allergic' but I have asthma and non-dairy coffee creamers affect me the same as milk does.

Familiarize yourself with all the milk related allergens and then check every label!

Casein or caseinate
Lactalbumen
Lactoglobulin
Lactose
Coffee-Mate, Prem, and Cool Whip contain casein or caseinate
Whey

Ther could be more. I got this from http://www.adrenalfatigue.org/sources-of-common-allergens/milk-allergens.html

I use Sugarshack's recipe & use non-dairy creamer for my liquid. It does contain sodium caseinate which is a milk derivative, but not a source of lactose. Just ask if they are allergic to the products you're using

You could try making SMBC and switching out the butter for HR shortening.

I make SMBC and up the granulated sugar by 1/2 c., sub some of the butter out for HR-short. and it holds up well in humidity. I have not tried making ALL with HR-short. but if you up the sugar a bit, then I believe it would still taste better than the non-dairy whip, which has chemical taste, IMHO.

my recipe for icing is as follows:

1 pound of shortening
1 1/2 cups of cake and pastry flour
(blend these together) then add
almost 2 bags of icing sugar (or more if needed)
1 1/3 cups of water
2 tsps of clear vanilla, 2 tsps of butter flavouring
sometimes i add a couple of drops of lemon and orange oil flavouring

mix for couple of minutes

this does not need refrigeration.

this makes the largest tupperware "thats-a-bowl" almost full of icing
and cake make several cakes

for the above recipe i forgot that you add about a teaspoon of salt - this cuts down on the sweetness

I have been making a little boys birthday cakes for years that are dairy and egg free and contain no nuts as he is allergic to all these ingredients. I make mmf from the recipe on here and the dairy free chocolate cake also from here. With the mmf just check the ingredients in the marshmallows but I have never had a problem

if you are making chocolate buttercream frosting I use black coffee instead of water. Gives the frosting a nice rich flavor and the same consistency of milk. Hope this helps

Bettercreme Ingredients: High fructose corn syrup, water, partially hydrogenated palm kernel oil, partially hydrogenated soybean oil, contains less than 2% of the following: Sodium Caseinate (a milk derivative), soy protein concentrate, polysorbate 60, carbohydrate gum, sugar, salt, artificial flavor, soy lecithin, polyglycerol esters of fatty acids, to preserve freshness (potassium sorbate), xanthan gum.

HTH