Moving Company Refuses To Unload Unless Paid Over Contract

LOCATION: Texas-Houston move to VA

We hired one of the biggest names in moving in the USA to facilitate our move from Houston, TX to Virginia.
They got half of the payment upfront and said the other half will be due upon delivery. What they didn’t disclose was that they are contracting out our move to their “sister company”. The “sister company” has botched our move and therefore we have informed the major company with whom we have the contract that they are in breach of our contract on multiple fronts. They have now cut the final payment to slightly less without much explanation. Turns out, the second half of payment which they are now reducing is the cut of their “sister company”. The owner of the company has called us 12 times today to say her drivers are not going to “work this way” and that the larger company is basically spending out of their pocket. We are expecting the truck to get to our place by 8pm tonight. What recourse do we have if they refused to unload our stuff WITHOUT much higher pay?
Side note: due to the logistics of move and life, I will be by myself when they arrive. I do NOT feel safe as I feel this will be quite a hostile environment (I’m a woman, mid-40s). I do not have family or acquaintances who can be present when the truck arrives due to the many times they have changed the time and date of delivery. What can I do in haste that ensures both my safety and the unloading of my items? Can I involve the local police department? Would they even take this issue on?
EDITED TO CHANGE “with” to “without” in the second to last paragraph.