Or house hack a 4-plex with the minimum down, and really stretch the rest.

For that area $950 to $1000 for a 1 bed is a stretch.

I am not sure how much experience you have outside of the triplex above, but if you don't have experience in something that big, it might be a stretch to sell someone on you being an experienced business partner to lead a deal that big. 

I have enough for up to a 20% down payment but that would stretch my finances fairly thin.

Your current income will be a stretch as a single parent.

There are plenty of properties out there, but if I can't find a couple of deals, I'll have to purchase at market value and most of the multi property homes in my area have been up on the MLS for pretty long stretches so I  doubt any of them will be jumping at a low offer.With financing, barely any of the properties would cash flow and the ones that would are in super sketchy areas. 

Just throwing numbers out there from a previous find, but there are a ton of places you can borrower the money from without needing to show personal income that would allow your savings to really stretch, and maximize your passive-income potential.

It's too small of a loan for the amount of overhead required to close the deal, especially to then stretch on the asset value.

They would likely NOT allow such a small loan stretched between two properties.  

Depending on your sourcing and work stills, that's a pretty large stretch, particularly given that VA inspections are more strict than any of the others.