Possibly, by having my mom 'gift' part of the down payment, but it would have to come from the money she'd make on the sale..

If she felt gifts were more important than rent, my guess is you did not adequately screen here application, or else your standards are very low.

While the philanthropic aspect of “reasonable housing” is laudable, at the end of the day (if you want to be successful - especially starting out) you need your properties to perform well.  

Will the portion the new people keep, be viewed as a gift? 

From the rest of her email, it sounds like for the purpose of making loans, that step is often rolled into the origination process and involves no out-of-pocket contribution from the customer (because they're making money off of making the loan, so they gift you the start-up funds). 

conventional loan, private money (family member) provided down payment as a "gift fund" which we separately negotiated lending terms.

If it bothers them or you that they get back more than what they gave you (aka interest) and have to pay taxes on the money they did actually make (aka fair) - well, you can compensate them for the tax on their interest (aka gift).The other options mentioned were:gift from them to you.

On the expense side, we have a "hospitality" expense line which includes gift cards, gifts for guests, gifts for repeat guests, or gifts when something goes wrong. 

first of all let me say, there is NO one size fits all when it comes to loan programs. what makes sense for you may not make sense for someone else, so take my opinions here as exactly that - my opinion. i am personally not a fan of DPA. reasons being the rates are always higher than traditional counterparts, and they're not usually even gifting you any money.

Hopefully they'll give me an early Christmas gift!