It will depend on more factors than we can go over here. Your income, assets, ratios, credit, your parents credit income assets etc. Projected rent can't be used as income, so you'll need to have enough to qualify for it vacant.
The only way to truly know the answer to your questions is to meet with a great local lender and discuss your plans. They can review your situation and see if there is a way to make this work, with or without your parents. If the answer is "no" you'll learn what you'll need to qualify for your next attempt. Best of luck.