Former is enticing because it will enable me to pay off one property and rental income will pay for the HELOC but then I still have HELOC on top of payment on a new home.   

I would argue that your duty as a human being at this time is to the children there and not the mother, and if you allow the situation to go on you're enabling an obviously unfit mother.

I have two options in front of me either to obtain a rehab loan, which will cost me $10k for six months ( points, fees, interest) or just finance the entire deal with my own money (cash).The rehab loan will enable me to obtain an additional property, so in six months i'll have two properties ( one with the loan, another with my cash)  but it'll cost me an extra $10k (on top of the regular down-payment which in any case i'll have to lay out) .

Practically you can search Zilllow's map with the school and crime layers enabled.

The most traditional avenue that most banks/credit unions will enable are the typical refinance (cash out refinance) to access equity. 

I'd prefer 10 year loan but I'd be willing to do 30 year if it enabled us to have another rental. 

@Ray Johnson great question -- we research and select the best available third-party real estate technology  providers and enter into exclusive relationships to create tech-enabled funds which give us a unique competitive edge designed to enhance returns to investors.

There isnt a whole lot that you can do as an investor, other than support programs that enable housing to be affordable, and be a part of those programs.

Two VA loans (one for each of us) were beneficial, and moving regularly enabled us to leave a trail of rental and flip houses behind.  

Currently renting both units with a CoCROI of 13.2% [taking all expenses including vacancy, CapEx, and property management (even though I'm currently managing it) into account].Currently living an extremely frugal lifestyle which is what enabled me to purchase this initial property.