This would be a question for a specialized tax lawyer who understands the tax law of your country and the country where you want to do your business. IMO just having a parents home in one place doesn't make a case for tax residency without formal proof such as a written rental contract. However, in the case of Boris Becker, having keys of his︀ parents/sister flat together with spending >183 days there was sufficient to condemn him by German︁ authorities.
I don't understand your second statement. I thought you want to prove that you︂ are tax resident in the country of your parent's home although you have or want︃ to have a business in another country. Now, you're saying that you want to prove︄ that you are not a tax resident in your home/birth country? Then, you will need︅ to prove that you have a tax residence somewhere else. In Germany, they have this︆ "perpetual traveller" rule which says that if you travel around and don't spend too much︇ time in Germany, you won't be considered a tax resident there anymore. But this is︈ a very weak rule I wouldn't count on.