The problem I ran into with the first bank (and confirmed by the second one who returned my phone call) was “to consider any income from 1099 self employment I would need a tax return for the past two years, and they would average the amount.

My wife and I want to buy another house in the same city using my second-tier entitlement.

My question is this:In negotiating with this lender for the second mortgage, how likely am I to be successful to work out a deal before the auction date?

I'd suggest option #1, but there's a second step that you haven't addressed.

She asked for a refund for that night, and I gave it to her, but I also refunded her the second night, even though we got the air conditioner fixed. 

Does it make sense to get a home equity loan on my first rental house to buy a second rental property?

Second, I am afraid the price of our home right now is at its peak estimated $635k and would like to use that equity money (roughly around $200k) to fuel my planned venture to financial freedom through real estate investing.

If you know who wants to sell and who wants to buy, you'll have the makings of a game plan in place that is second to none.

Bought our first rental property late last year- a vacant, second floor 2 BR, bank owned condominium. 

Not sure how my business is going to go this year but assuming I have $2k month self employment income, no debt, $50k cash reserve, and an excellent credit score...What is the likelihood that I will qualify for a mortgage?