There might be some "undocumented features" in this job, Phoenix, which could prove good or bad - and your trial run will highlight them for you.
If you get on well with the whole family, and they are "good people" who need someone capable in the position, able to see when father is in danger of making a mistake and sort it out tactfully, you could end up running the whole show in a short while. If so, you should get a suitable remuneration for your input.
If the business is in a bad way because of father being a bit vague, you could end up doing the lot and not having any job at all at the end if it all fails.
I'd say you need you be businesslike with the boss as well as with the job. If you can do it without falling out with him, he will accept your expertise and you will work well together. If he resents you putting him right, there will be tears before bedtime.
Watch out for all that "housekeeping", it could be a translation of "skivvy and dogsbody" Are any cleaners employed?