When the swamp cooler needed repairing/possibly replacing in one of the units, I asked the tenant if she was interested in getting AC and she said she wouldn't be able to afford the electricity  and preferred to keep the swamp cooler.  

If they are only seeking a check every month and the largest amount possible based on the equity of this other property then sure it's a fine decision.A couple other thoughts though:With a smaller multi-family a vacancy is felt more financially than with a larger one, but the extent of that is influenced by the market's local metro and property location; andWhy not use some of the equity from the property to fund the purchase of the smaller one and then have two properties generate (probably) the same amount of income or more with debt service on both.  

Have a wait list of possible tenants in the case of vacancy.

I felt like it should be possible that this could somehow be worked out through the title company that did the closing.

I'm not sure if I would be able to have the winning bid when it comes to auction - so I'm trying to consider as many things as possible.

Which is the best and is it possible to get funding without using your money

Congratulations on the possible duplex. 

all are possible just depends on your business model.

She's facing possible foreclosure (not sure how far behind she is) on a 70-acre property located in Colorado.

This can have a possible trickle down affect to surrounding areas in Kansas City.