Do I need to go to Georgia to get a letter of executorship or can I get one in the state where I live?

Please accept my condolences on the loss of your mother. As for your question: if your mother had her principal residence in Georgia, then the county where she had that residence is the county where you must offer her Will for probate, if it shows up, or where you must open her estate for administration if no Will can be found. You cannot do a Texas probate if she didn't live there. The fact that she was visiting you there does not matter. Now, if you believe that she had changed her principal residence to Texas or another state other than Georgia, then the fact that she owns the house here does not mean you have to do the probate here. In short, a critical question is where your mother had her principal residence and whether she had changed it before her death. An experienced probate attorney should be able to help you answer that question, but you look at things like where she filed her tax returns, where her driver's license was issued, where she voted, where she had most of her doctors and other service providers, etc. However, if you find an experienced probate attorney here, that attorney should be able to work with you to get the estate opened and you appointed as Executor or Administrator with very little need for you to actually travel to Georgia. I, personally, have worked with a number of different out-of-state clients on Georgia probate matters. It's not usually that big an issue. So, find an attorney who works in the county where your mother had her principal residence, schedule a consultation (by phone if needed), and get the attorney to help you figure out the next steps. Best wishes to you.