ANSWER - Damn right you can. All traditions started somewhere. Take Wicca for example, its only about 60 years old and there are estimated to be over a million adherents worldwide already. All traditions have a starting point in time. It is easy to fall into the trap that something must be old to be taken seriously but there is a lot of value in fresh innovative ideas and some old traditions can get jaded and lose their meaning (*cough* Christianity...). I dislike the idea that if an idea cannot be traced back to ancient roots it is not worth bothering with. Many witches have modern ways of doing things and its great that the craft is a living evolving entity, not some stuffy anachronism stuck in the pages of some dusty grimoire. Witchcraft would get boring pretty quickly if it never changed!
But I'm not sure what you would be doing is so much starting a tradition as formalising existing beliefs and practises into a structure. You speak of being experienced so no doubt you already work with established practises in a way that have meaning to you and your family. You already have the confidence to know that what you are doing works well for you and yours so taking the fruits of your efforts and experience and weaving them into a tradition that can be handed down through the generations of your family makes sound common sense. No doubt future generations will tweak and mould the legacy you leave them but again that is the evolution of your tradition that will keep it alive for those who follow your path.
I think its a wonderful idea and your ancestors are lucky that you care enough to share your journey with them.