I am between a rock and a hard place. I am seeking financial advice and help to pay for my mom's LTC.

Didn’t see it mentioned in your post.
Is your mom medically qualified for Medicaid? She must be deemed both financially and medically in need of assistance.

What was the reason your mom was denied Medicaid?

Applying for Medicaid is a daunting task. I suggest you find the facility you'd like for your mom, do the tour, talk to the financial people, and then get in contact with their social worker. Every facility has at least one social worker. Ask the social worker to help you navigate the Medicaid system. But you will have to commit to a facility in order to avail yourself of their services.

This is what I did when my dad needed Medicaid for a nursing home. I had to do all the foot work but the social worker at the facility took me through the process step by step.