I'm sure there are some people who get 'persuaded' into care homes by 'well-meaning' relatives, and others that have no choice because they can't get the amount of care they need in their own home. It's brilliant for your grandma that she has you two looking out for her needs every day. Lots of people have nothing like that. It sounds like she's getting the level of care that's right for her current needs. However it sounds like she's getting so many different carers (which unfortunately seems to be the norm these days) that, experienced or not, I don't see how this one carer could possible build up enough knowledge of what's going on with your grandma to be bringing up care homes at all. When that time arrives it would when family members were concerned and consultants and social workers get involved in talking about it. Nobody in the UK can be 'forced' by the authorities into a care home if they're able to understand the reality they're faced with and can respond/deal with it. If the situation does arise hopefully they would have loving caring family, like you and your mum, that will be able to persuade them that it's the only path to now take and be with them through that.
Of course, it's a whole different ball game when it comes to sectioning someone. Then specific rules come in, but even then you couldn't force somebody into a home. They're placed somewhere, usually a hospital, to be assessed and if sectioned it's a pretty short period before this has to be reviewed. Following on from this the sectioning might be revoked, extended to another period of the same time and again reviewed, or unfortunately a Section 3 may follow if it's felt that is what is required. It's a Section 3 when the dreaded 'deprivation of liberty' kicks in. With this a person is not allowed to return to live in their own home or anybody elses' because the danger to themselves is too high. They need secure care. Even so, there are many regulations and legislations that are in place and the deprivation of liberty is regularly reviewed.
I would agree with another poster that it would be a good idea to research care homes and think about what you would want in that case, but that's only because you'd have an idea of what's out there and then you can put it out of your mind.