Any person who is employed (even part-time) should have a contract, charity or not. I'm not sure, but I think it's a bit dubious for some duties to be part of a contract of employment, and some as a self-employed person, which is what I think you're saying, UNLESS these duties are very different e.g. some about caretaking and some about, for example, management training (but I'm not an expert in employment law, so you'd need to check this out further). If the duties do all come into 'caretaking', it would probably be better for the charity to formalise those duties with a single job description and a contract of employment for that job.
I also think your friend is very right to be concerned about the fact this employee is a relative of a trustee. The married trustee would have a 'conflict of interest'. This Charity Commission guidance says that:
"Conflicts of interest usually arise where either:
- there is a potential financial or measurable benefit directly to a trustee, or indirectly through a connected person" - spouses are 'connected persons'
and
"Trustees can only benefit from their charity where there is an explicit authority in place before any decision conferring trustee benefit is made.
Examples of benefits to trustees are where the trustees decide to:
- employ a trustee’s spouse or other close relative at the charity [...]"
So the charity would have had to specifically get authority before the person is employed or paid. Authority will come either from a clause in the charity’s governing document or by asking the Charity Commission for permission. If they haven't done either of these things, they're acting illegally.
I suggest your friend take a look through this guidance, too (and any other associated documents) from the Charity Commission website - most are written in a pretty easy to understand way - and, really, she should have ben given this sort of information when she agreed to become a trustee, as part of the induction, particularly as there are other legal liabilities too.
I'm sure they/she'll be able to take advice and get it sorted, though - as long as they're dealing with it there's no need to panic.
(I'm a chair of a charity and give advice to charities on governance)