Butter is a monounsaturated fat. So as other ingredients in processed food, or economy for the homemaker goes, its a better choice than most fats. If proteins in dairy cause problem, try ghee instead.
It is not VEGAN however.
But the commercially available coconut and palm oils leave a lot to be desired (due to their processing). If you have an african market in your town, you should be able to get a GOOD quality palm oil (it will be a bright orange color).
Also eggs are NOT vegan. Not really sure what your 'doc reason is.
1T Flaxseed meal/Slippery Elm bark powder to 1T hot water, mixed, equals 1 Egg.