Traveling between UK and US every six months without without visiting home country

[RGuptaa 0]

I am sure there are many of us in a similar situation where Parents cannot be left alone in the home country, please share your experience. Here is my current situation.

I am a green card holder living in the USA since 2006. My brother is planning to move to either Canada or U.K next year from India. Currently, he lives in India with his spouse, kids, and our Mother. If my brother moves to either the U.K or Canada, it will not be feasible for my mother to live alone in India. So we are exploring options to either permanently immigrate her with us or any other arrangement such as making her travel between UK/Canada and the USA every six months. My mother already holds a USA B1/B2 visa which is valid until 2029 and she has already visited me multiple times in the USA before the Pandemic.

Scenario 1  (Long term Visitor's visa)

1. Do you see complication(s) getting her Long term Visitor Visas for either U.K or Canada?
2. Let's say she gets the Visitor's visa. In that case, can she travel every six months (180 days)between UK/Canada and the USA?
3. Do you think it is feasible to travel between UK and US every six months over a period a of 5 years without going to home country?
4. Is it required for the visitor to live in Home country before re-entering USA?
5. How likely it is that immigration can stop a visitor to enter the country if he/she is traveling between USA and Canada/U.K  without traveling to the Home country in between.

Scenario 2 (Short term Visitor's visa)

1. In case she doesn't get the long-term Visitor's visa for U.K and Canada, can she apply for the Visitor's visas for these countries while she is in the USA and how likely is it to get it? The idea is to avoid her traveling alone to India.

[pontevecchio 12]

Become a US Citizen and sponsor her for the GC.