Any profit split varies depending if your relative just gives you money or also helps you physically. 

just take a QC  and transfer the legal description from current deed.. and have your relative deed to you. and if there is a place for consideration just put 10.00... its on the county transfer form that you need to describe its between relatives not on the deed itself.. at least I have never seen it on a QC and I have done them in many many states.

This means YOU occupy it, not your relatives, co-workers, renters, or bums off the street.

So, you would be essentially buying out your relatives with a loan of $500K, and your portion would be the remaining $100k in equity.

OR you probably need your relatives to step in here to help. 

Do your relatives want to be equity partners or just the lenders?

I love that you saw an opportunity to both help your relatives and create some multi-generational wealth.

Best to ask your loan officer because there are so many ifs, and but whens involved in qualification guidelines.Not sure why your relative doesn't want to disclose the terms (tax liability?)

The problem is you're still legally obligated to pay that debt if she doesn't, regardless of what your relative told you in her text messages. 

If you feel you must worry, worry instead that your all-cash offers are as low as possible (because you'd be paying cash), and, that your juggling with your relatives' HELOCs will proceed smoothly, in a timely fashion.