No, you both would not have to live there with this arrangement.

My preference since my reputation with the seller is on the line is if possible to arrange seller financing on both sides.

Forgive me if this questions has been asked, I did search but couldn't find an answer directly related to our situation.
Preface -
My parents owns a lake house on Lake LBJ. The property has 6 bedrooms and can sleep ...

I was just wanting to see if this partnership arrangement sounded fair and or if anyone as any better ideas.   

Ask yourself: why would a landlord do this arrangement with you?

There’s nothing about this arrangement in the Lease that I know of.  

@Mason Hickman lol too funny@Craig Parsons - I think mason alluded to this, but if you did move forward with this arrangement, you need clear rules and regulations so their residency does not affect other tenants day to day life and repercussions if they are abused. 

I can't speak to the legality of the situation because I'm honestly not smart enough about it but I have been the assignee in such an arrangement.

@Sheng Rao I arrange commercial financing for clients in Canada and can educate you on guidelines.

Does the buyer arrange for contractors to come to see your property without there being an agreed time frame like hey I’m going to have these people come out I would appreciate if you gave me x amount of days before talking to another buyer ?