There are two reasons given in the question for wanting the visa: to help and to comfort. I agree with what you say as far a help such as babysitting is concerned. However, the UK visitor visa is not just for tourism. The permitted reasons do include visiting family. Cannot the mother come to comfort her daughter, giving emotional support and companionship, if she does not do babysitting or similar services?

But she is going to do that

Not the answer he wanted but the answer he needed to hear.

I see nothing in the question that says the grandmother will claim to be on vacation. There is no such thing as a "tourist visa" to the UK.

@LightnessRaceswithMonica I am suggesting not having the mother do normally paid work. The family can either pay for baby sitting or ask local friends and neighbors for help.

A good notion but I got the impression that was not feasible, hence the question

@PatriciaShanahan You're making a compassion argument. I think that is wonderful!

@DavidRicherby That's fixed. Sorry for the typo! So what will the grandmother claim?

@DavidRicherby The grandmother would claim she is visiting her daughter at a time when the daughter urgently needs emotional support. The official overview lists "to see your family and friends" as an appropriate use of a Standard Visitor visa.

@PatriciaShanahan whoops, you lifted it out of context. Context is "for leisure, for example on holiday or to see your family and friends". When you see words after "for example", that means they clarify the preceding term, not extend it.

@Harper-ReinstateMonica Thanks. I agree that the "for example" makes it absolutely clear that visiting friends and family is a form of leisure travel and as such included in the visitor visa purposes.

@PatriciaShanahan I didn't mean that, but your optimism is positively inspirational!

Quoting from gov.uk/standard-visitor-visa, one valid application basis is "for leisure, for example on holiday or to see your family and friends". I would say that if everything is as the OP says, the mother-in-law has a legitimate basis to visit her daughter (his wife) – whether to comfort her or not is irrelevent – but not to work ("help").

The Border Force will almost certainly count the mother-in-law's "help" as paid work, in particular because she will almost certainly be given food and board by the ones she is "helping". If they get help elsewhere and the mother-in-law does not work, they could try applying. Of course, anything written on the visa application or said at the border controls which is perceived as an attempt to play the system will be met with extreme prejudice and an almost certain deportation.

@Toothbrush However, that reason for visiting also needs to make sense. "Comfort" alone does not explain the desire for an extended stay, and OP hasn't explicitly said this, but I gather OP wants help indefinitely; or at least for more than a couple of weeks.

@JBentley Ask Parliament, I didn't write it. I can't really explain how immigration works in a comment. The upshot is it's not a right! Border guards worldwide follow this rule: presume unlawful intent and allow them to disprove it. Saying "I'm here to work as an in-home caregiver" is a weak hand. Evading saying that is much worse.

Your citations are for people looking for Indefinite Leave to Remain. The grandmother isn't looking for that, she's looking to visit her daughter and grandchild on a temporary basis. This is a totally legitimate use of a Visitor visa, to visit family is explicitly one of the uses. Where are you getting that a Visitor visa is only for a "vacation" (an American term, odd to use in UK) or only valid for a short 7 day visit? It may be reasonable to say not to phrase application as "I want to employ my MIL as a nanny" but most of this answer is pulling stuff from thin air that simply isn't there.

@Harper-ReinstateMonica From my experience, and also from friends experiences, I'd say that at least the UK Border Force does not seem to work under any presumption of unlawful intent, they seem to be sensible people who have no problem understanding why a close family member would visit for extended periods of time just to spend time with family.

We can argue about this for a long time. I suspect that her admission depends on exactly what is said on the application, and only a lawyer is going to give us a really good answer.

@IvanMcA Because my understanding of OP is that their need is long-term. Therefore they will need assistance long-term, unless they plan to rotate different family members in from time to time. With immigration, it is folly to pursue a short-term solution when you need a long one. That will paint you into a corner.

@HansOlsson Oh, they do it, just very transparently to those whose demographics create low risk. They know you or I can get halfway respectable work in our home countries; so they're not worried about us coming to UK and joining the underground labor market or going on the dole. Also your immigration history is part of it, and yeah, it happens that fast.