Hi Murphy,
Mom is not intentionally trying to embarrass you. As her disease slowly robs self-awareness, she becomes less inhibited, losing both memory of how she once behaved as well as a sense of social norms. Think of it as it’s as if an internal filter on what’s polite behavior or not is turned off. It is important not to think of times that mom is acting out of the norm as “misbehaving.” She is living with a disease that is damaging their brain. Take the strangers aside and explain the situation. You may also consider creating a business type of card that say something like “Thank you for your understanding, my mom is living with Alzheimer’s disease.” You can hand these to a waitress or clerk to help them understand. Embrace that your mother is still well enough to spend time out in public with you, look at the positive that you two can enjoy your day out together just try to have some more patience and love with mom.