Sorry to hear you are having difficulties but I am here to help. Keep in mind the answers I give depend entirely on the responses you give in return. So please be insightful and patient and maybe together we can solve your problem. Realizing the answers may not be pleasant for you to hear but you are requesting my expertise and I hope you will honor your good faith promise.
How are you retrieving your signal? Are you using a converter box? Do you have access to an external audio amplifier?
Do you mean you hook the cable directly to the tv or do you mean you have Direct TV satellite service and using a converter?
If mom is in a retirement home I do not think we need to be making enough sound for her to hear it by using external audio amplifiers. However there are many options available to her, i.e. wireless headphones, wireless speaker systems, or if she is using hearing aids the newer technology is looping which may already be provided by the nursing home. Ask them if they are looping.
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The set is producing as much sound that it is capable of. This is why I have suggested these other solutions. I am sorry you are frustrated with the audio level of your designed equipment however, not every tv is designed with super audio amplification and the use of large speakers. When the consumer requests smaller tv's generally you are receiving smaller speaker systems and less accommodating audio level. That is why these viable options are your only solutions. As you will recall my statement "Realizing the answers may not be pleasant for you to hear but you are requesting my expertise and I hope you will honor your good faith promise."