tl;dr: You could afford a minimum of an 8 year term loan with your dad at 2.99% instead of PMI, and it would be in your (financial) best interest to do this.
Mathematically, if you could get anywhere between an 8 and 30-year term loan from your dad at the same rate as the mortgage, and thus avoid paying PMI, then it's a no-brainer.
As mentioned in mhoran_psprep's answer, you'll need to disclose the loan when you apply for the mortgage along with all other debts, but if you would have been approved for a 90% LTV mortgage, you'll definitely still be approved for an 80% LTV mortgage; it's much less risk for the bank at 80% which is why they don't require PMI below that point.
As for calculating how short your term loan with your dad could be, an average cost of PMI might be around $250/month for a loan of your size. A 30 year loan of $35K at 2.99% has a monthly payment of about $150, meaning your monthly payment for that portion of the mortgage, in comparison to not having it, would be around $400 per month. That would be pretty close to a 8 year term loan with your dad at 2.99%.
Side Note: You mentioned you thought you could afford to pay off the loan in 15 years instead of 30. Definitely check to see how much you can save on the rate with a 15-year loan. If it's significantly cheaper it may be worth it, as long as you're reasonably sure you'll always be able to continue paying it.
Way off to the Side Note: friends and family relationships are often hurt by personal loans that go bad. If there's even a small chance that you could ever default on your dad's loan, and if that might hurt your relationship, then it may be worth avoiding just because of that.