Residence visa, UK citizens, mother and son.

Hi and welcome to the forum from me.

I'm going to hazard a guess here and say yes, I think you would have problems. To the best of my knowledge, you won't be able to lodge a joint visa application because you won't satisfy any criteria I'm aware of which would allow for financial or other dependency to be a factor. Either you'd need to be a minor or in some way incapacitated (if it were to work that way round), or you'd have to be demonstrably financially supporting your mother. 

If you couldn't both meet the requirements independently, it looks to me like a non-runner. But I am very much a layperson (albeit reasonably well self-informed through longstanding residence and keeping up with news and information on immigration and other matters), as opposed to any sort of professional advisor.

Maybe some other poster(s) could provide some grounds for optimism, if any exist.

As well as seeking professional advice re the visa application, I would also be sure to also seek advice in advance about medical insurance for a 89 year old. Showing you have some private health insurance is part of the visa process, so I would also run your mother’s application past one or the insurance or medical advice people who are affiliated with this website.