My partner lives with me, but I pay for 95% of utilities, etc. as well as all furnishings, remodel, etc. 

Create a thorough remodeling schedule and budget, choose reputable contractors, secure licenses, and supervise the work.9.

We completely remodeled the kitchen and rest of the house but think we will leave the bathroom alone for now since it’s not within budget to renovate.

It's really hard to remodel, flip, or BRRRR real estate and pay top end labor prices.

Can someone provide me with some financing ideas other than the two that I just mentioned that would enable the other heir to receive cash from their portion of the equity based on its current assessed value and allow me to take ownership of the home, subsequently remodel it, and rent it?

Think about the timing of this scenario (there are many): current guest checks out at 11 am and next guest is arriving in at 3 pm, the cleaning person who starts cleaning at 11 am discovers a broken kitchen faucet or a running toilet around 11:45 am.

They should be doing at least 2-4 full remodels on their own per year on the high end.

Learned how to fix a sink and change a toilet!

I'll play devil's advocate, at that price you might as well invest in multifamily units. 3-4 unit properties are selling in the low $200K and with an average rent of $700/unit, you get better cash flow and spread out risk (1/3 units vacant versus the house 100% vacant.)You do your inspections and make necessary improvements upfront to offset the risks with buying a "used" property instead of brand new construction.Alternatively, how much of a price difference between new construction and a remodeled home?

Weigh these with the time to manage a long distance team and travel to look at properties, check on remodel progress, and property condition after renovation.