One gotcha for the FHA loan program when buying a 3 to 4 family is the self sufficiency test where you take 75% of all the units (including the once you occupy) which has to be equal or greater than the PITI (principal interest taxes insurance and PMI)

She could be self-sufficient and off all government welfare within three months and, if she's really willing to work hard, could even have some money saved up. 

Back to the original question - I think one LLC would be sufficient in this case, it allows you to have the appropriate protection and minimizes the operating costs of the LLC.

As long as there is sufficient cash flow and you maintain reserve capital, leverage can be a great tool that allows for exponential growth.

From what I've uncovered after speaking with some local lenders it's possible to obtain residential mortgages through an LLC, however lenders won't consider it unless you've been able to demonstrate positive income (by means of tax filings x 2 years) sufficient to cover the added expense of the new property. 

And in any event, because multi-family data is found in less quantity and quality than would be ideal (far from it in your case) an appraisal of such properties will always be weak.Here is my advice for the future - ignore almost everything in the appraisal with exception to two things.

LegalZoom is sufficient for setting up a single-member LLC without any variations.

Also, I think a part of the original question was not quite answered: do I NEED the additional coverage, or is Airbnb’s coverage going to be sufficient, or is this just a question of risk tolerance?

Some amount of day-job income will typically be needed to offset that, and if the person maxed out their DTI when they purchased their primary residence, and needed a cosigner to make the purchase of the rental work, there often isn't sufficient day-job income left over to cover that gap.

Here in the SF Bay Area (also HCOL), 3-4 unit properties at MLS prices do not pass the FHA self-sufficiency test, more or less as a hard and fast rule.