Me and my wife are planning to purchase her mom's house. 

Let's just ignore the fundamentals of the real estate and/or negotiating a good basis in property we purchase and focus solely on how we can acquire real estate without any of our own money.

Or, would they owe what the 3rd party had paid to purchase the property from the bank?

Purchase price: $1,900,000 Cash invested: $900,000 The 1.64-acre tract at 150-190 Hanes Mill Court is across from Walmart and many major retailers located off of a many thoroughfare .

I am interested in purchasing a seasonal short term rental as a replacement ($500,000). 

Yes, we have been doing lease/purchase and lease-options deals for over two decades.The rent+own strategy is particularly relevant when prospective buyers are having a hard time qualifying for a mortgage, either because mortgage rates are high or because prices are rising.Kinda sounds like both are happening right now, doesn't it? 

Purchase price: $300,000 Cash invested: $70,000 Sale price: $450,000 BRRR method using an STR property that has projections in the 75k gross rangeUPDATE -- did rent well.

You will borrow money (your equity) in order to qualify to borrow money to purchase, which means you are 100% leveraged.

We have an influx of people coming in who are associated with the program that are purchasing and renting.

Purchase price: $130,000 Cash invested: $20,000 Didn't expect my 2 bedroom rental to rent for what it did.