The taxation of family companies is a complex affair and you really need to talk to an accountant who knows all the details of your family company. But I think what's going on here is:
- The limited company is a "close company" - i.e. a company owned/controlled by shareholders who are related to one another.
- There are various rules in place to prevent close companies being run in a way that seeks to evade or avoid tax. In particular, if value is transferred from the company to a shareholder or to an associate of a shareholder, that tends to get taxed in the hands of the recipient as if it they had received a dividend from the company, even if the transfer of value isn't actually structured as a dividend.
- Your mother and brother are getting free accommodation in a house that neither of them owns. That's a transfer of value; the value transferred is the amount of rent the company would get if it let out the house in an arm's-length transaction at the market rent. Your mother is getting 50% of that transfer.
- I assume your mother is either a shareholder in the company or an associate (family member) of a shareholder.
- Therefore, the concern is, your mother is going to be treated as receiving a dividend every year equal to 50% of the market rent the house would fetch. (Also the company needs to pay dividend withholding tax on the same amount, for which your mother will get a credit.)
- She can avoid this by paying the market rent for the house, which is what is being suggested.
Another possibility that could be explored would be for your mother to become a director of the company, but this is not something to be done lightly — directors have serious duties, responsibilities and potential liablities.
Talk to the accountant that looks after the company's tax affairs. If the company hasn't been getting professional tax advice up to now, then it's time to start getting it.