We are getting ready to take a HELOC out on our primary residence.

The VA loan considers 1-4 unit properties as the same thing, so as long as you plan to occupy the 4plex you want to buy next year as your primary residence (which would mean selling moms house that you inherited, or turning that house into a rental). 

My issue right now with buying my own home or house hacking is that I don't want to be tied to a primary residence for a year, using an FHA loan, if career opportunities present themselves out of state or even in different regions of the state.

Generally a HELOC can get you a down payment for the property, but generally not a whole property, it would probably make more sense to get the financing for any rental traditionally as it will probably have more favorable terms. 

We purchased our primary residence about a year ago and have been building out a basement apartment we will be renting out to my mother in law.

I have equity in my primary residents, so I plan to start with that.I owe about $124k and it should be worth 165 - 175.

On a related note, I was planning on traditional lending with a 20% down payment.

Not as good of terms as traditional mortgages, but still leverage ability.

I am unable to use a traditional cash out refinance due to unquantifiable DTI ratios.

If you and the property qualify, a traditional mortgage is likely to be the cheapest money you'll find.