Should I ask my mom for my 1/4th and come up with money to put a trailer on it and begin renting it out - but then again that could be a large financial strain until I have more working capital?

It can be a very strained family get together if they aren't paying or if you evicted them for not paying.

This allows you to let them get that realization that they can cause themselves financial strain.5.) 

Most of these houses lack insulation, have old single pane windows, have galvanized/copper/cast iron/PVC plumbing all in the same house, post-n-knob electric or cloth wiring or both, and lots of bad remodeling done over the years.

I had a break into one of mybhouses years ago and they can through the back window. no one was hurt and I replaced a window pane.

If the unit is well-sealed(you can check for drafts by walking around with a candle and seeing if/when the flame blows(super-cheap way,) or get an energy inspection(more $$)) and insulated(double-pane windows at least, proper wall insulation- and maybe ceiling too?

Single pane windows are ok if have storm windows.

This is currently a rather inefficient building with single pane windows and drafty doors we intend to replace over the next few years and I'm concerned another record cold snap could trigger the same issue again in the near future. 

If the deal might be big and your credit can't take the strain, perhaps you're better sticking to your current mortgage and doing the investment on its own or doing the refi and socking away the cash saved until you're in a better position cash-wise or credit-wise.

as a general rule, every property had some issues, so tapping out a window pane, or etc.