I agree that an appropriately trained family member training you is adequate -- it doesn't need to be a nurse, provided that the family member is experienced in all of the things that you're going to be doing, which if this is a long-term case, the family member is probably as good or better than any of the nurses that could train you.
I also do a lot of my own research (often at work during downtime) regarding equipment, supplies, and cares. YouTube is full of all kinds of videos, and manufacturer websites typically have downloadable equipment manuals so you can learn about settings, maintenance, troubleshooting, etc. I also find a lot of Powerpoint presentations on various issues are posted as part of CEU presentations, etc.
When it comes to housework/meal prep, I would tell the family that since you're a new nurse and new to this case, you'd like to concentrate all your time in the house on learning all about your patient's care, getting comfortable with the routines, making sure you're not missing anything, making your charting accurate, etc., and if you spend time doing non-nursing things while you're there, it will take away from your learning things completely and properly. I don't see how they could argue with that logic, and by the time you're an "experienced nurse" on the case, they'll already be used to you not performing those types of duties.
And for charting, I liked reading the past charting from other nurses. Not only did it help me see what types of things were expected in my charting, but it also helped me to see how other nurses organized their workflow.... did they do the breathing treatment before or after the bed bath? Vitals before, during, or after a tube feeding (or all three)?