To the seller, it implies there is no chance a lender will pull out at the last minute and jeopardize the deal.Realistically, most wholesale deals are negotiated well in advance, so all parties know where the money is coming from. 

A decent spread and 3 happy parties Lessons learned?

It's a win-win for both parties depending on the price. 

If it is that simple, do we receive cash from the the mortgage holder/bank and then just pay off the first two parties via cash?

I work for a third party auction company in Texas and though a month or two may not seem like it isn't enough time, it actually is if you have your buyer list available. 

A real estate attorney can assist with drafting a partnership agreement that outlines the rights and responsibilities of each party and addresses any potential contingencies.

FCI covers almost every state, are not overly expensive, but they are a big company and sometimes the different parties don't communicate well with each other.I have also used Allied and August servicing with good results.

Sell the entirety to yourself (through an unrelated party) and do a 1031 on that sale. 

I recommend having a local experienced investor (an unbiased party not someone trying to sell you something) do a detailed video tour of the property and the street/neighborhood before you submit an offer and paying them for their time $100 or $150.

The third-party appraisal came in at $110,000 so regardless of if you "know" the property is "worth 120-140ish" , we can not lend based on your opinion and must utilize an independent-third party value.