1) will your parents be paying any sort of rent (I assume they are not buying the current home from you)? If so then a lender will probably look at home #1 as an investment property and you may need to formalize a rental agreement to show what income you will have for home #1.
2) Is your income suffcient that you can easily qualify for a 2nd home without any rental income from home #1? If so, it will not matter and I suspect there will be several lenders glad to do business with you.
3) What does your credit history look like? Again, if you have sterling credit, and income sufficient to carry both homes, then it should not be difficult.
Assuming you move forward, another issue you will want to discuss is the property insurance for home #1 - it will no longer be "owner occupied" when you move out so you will want to make sure the insurance policy is appropriate for the situration. Thanks goodness your parents have you - many of our elderly are not so well cared for - I wish you well.