Buying a house with my kids?

[Daniel Murphy]

Okay, so this is a rabbit trail post but... 

I'm going through a divorce & looking for options to pay my soon-to-be ex out.  I may be forced to sell my primary home as I can't get a line of credit large enough to pay her out.  If I sell, I likely won't have enough money for a down payment on the next house. 

But... My 3 kids (15, 17 & 19) each have a large enough chunk of money that if we put it all together, we could make it happen.  I just don't know how it would work to structure the ownership & finances.  

Hypothetically, they would have the money to put down, but I would be paying the mortgage & doing all improvements.  So how would I account for their share of appreciation in the future? Ownership structure etc.? 
Rabbit trail, for sure.  Feel free to tell me all the ways why this is a stupid idea.