I know that if we are going to start a business, it is crucial to keep aside some liquid cash to fund the business at least for a year.

On one hand I want to suggest looking into opening a HELOC on your current home rather than selling, this will give you access to some capital for your down payment funds on your next purchase and not require you to move into a rental for a short amount of time as you transition (something i'm guessing wouldn't be extremely fun especially with a little one either on the way or just arrived).Once you have adequate down payment funds, you could simply watch for the right thing to come along from the comfort of your own home.

get your funding before you make promises to buy properties unless they are nothing but empty lies.

A second home will allow a higher LTV, but you won't be able to count any rental income to help you qualify, although from your post it doesn't seem like that's an issue.Homestyle is available for 1 unit second homes and investment properties. 

I am considering funding the purchase with HML and then the rehab costs with a personal loan (~13% interest rate, no money down). 

It has a small mixed-use component that works with FHA funding. 

ARV $183,000Initial Purchase $67,200Rehab costs ~$13,000Total cost in the property with purchase and rehab $80,200Allowable cash out with 75% LTV $137,250Closing costs were around $5,000Cash at refi closing was around $132,250Excess cash above what was initially invested($132,500-$80,000)= $52,250!

I've heard things like tax debt, remarriage, and sadly a senior couple who could no longer live alone.part of that Is the wet closings you do we do dry closings.. we sign anywhere from 1 week to a few days before the actual recording of the deeds.. then funds are dispersed the next day.. no one gets checks on the spot like you guys do.. 

So if you come along and offer them 1st position collateral at a ridiculously low LTV as you've described, AND say, 6% interest on their money for up to 8 months or a year...

For instance, if our imaginary apartment building qualified for 80% LTV financing, but the industrial building only qualified for 70% LTV financing, then the apartment building might be able to generate a higher COC return than the industrial building due to the financing options.