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My suggestion would be Biotene for mouth rinses, as it has a neutral pH that will protect gum tissues. I would also encourage chewing sugar free gum, if it is tolerated well. This will keep salivary flow higher and contribute to breaking down plaque accumulation. I find softer diet are the main culprit here, as the food tends to attach more readily to the enamel and root structures and exacerbate the gingivitis. I have treated homebound patients in the past and this is the best option, visiting every three months. However, it sounds like this is not a possibility for you. Hope this information provides you with some guidance.
I don't personally know any hygienists that make house calls but you could send requests to your local dental community and see if someone would be available to assist your Mom. I recommend a daily dose of prunes as it helps my Mother-in-law with her regularity. Gum should not affect the GI issue at all. Any smoothie drinks would probably considered sticky, especially if you notice material clinging to glasses or cups. That would mimic what happens on the surfaces of her teeth. I would still try the Water Pic but keep the tip in her cheeks to avoid any gag reflex. It would service your Mom the best.