I was interested in a house that was bank-owned property. The property was in NC, the bank whom owns it is in TX. My Realtor sent the documents over to the bank's Realtor. He never received proof she sent it to the bank. Just they were 'looking it over.' The price lowered while my contract was supposedly sitting at the TX bank. I re-submitted another contract for the lower price, and still no proof that the TX bank received the offer. Just a message from the other Realtor' they would not accept the contract, so once again, I submitted another contact to the letter of what the bank wanted. My Realtor told me what I needed to do and we met up on Saturday to sign the papers again. He told me all offers must go through the 'other Realtor' and she said if anyone calls over the weekend she will them them it is under contract.
On Monday, my Realtor took the paperwork to the 'other Realtor' and she said she should hear something back in a day or two. Again, no proof she sent the paperwork off.
On Friday morning, my Realtor called me to tell me the someone made a cash offer on the house I wanted and the 'other Realtor' accepted the offer.
Do I have any recourse to sue the 'other Realtor"?

Not the way you describe the events. Banks who own foreclosures are notorious for doing all sorts of sloppy and contradictory things. You don't say that you have a contract signed by both parties, just your offer(s) signed by you. Maybe your realtor shouldn't have said she would tell others it was under contract, but what she probably meant was that they wouldn't show it while a solid offer was in. It stands to reason that the bank is going to take a cash offer over a loan.
Now if you find out later that something went on with a deal with a friend or someone connected to either realtor, and that they were deliberately stalling, then you can sue. But you need evidence, and the burden is on you. It does happen but is hard to prove.

Thank you so much for your insight. It has helped me tremendously. Hopefully, I can get past this and find something else that is close to my dream home as that one was. I didn't think I could do anything, but I had to ask. Thank you for your prompt response.

I agree, not as your story goes, they are not required to accept offers, and that is why often phone calls and follow ups should be done, I would ask why your realitor was not talking to that realitor on phone often.
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Your realitor is to protect you