Is the money earned from selling a shop that I inherited from my father—after he had bought it from its owner for a specific price, and then I sold it to another party for a higher price—considered to have a trace of doubt (shubha)?

If what transpired between you and the buyer was merely a promise to sell him the property if you were to purchase it, and you did not sell him the property before acquiring ownership of it, then there is no harm in that. You may sell it after you purchase it from its owner, and even if you sell it for more than you bought it for, there is no sin upon you in benefiting from the profit you earned.