Back in 2004, I went to the USA for 5 weeks and my sister ran my website for me. She was 14 at the time. She went to school, came home, printed the orders, e-mailed customers, telephoned customers and packed the orders, my mum then took them to the post office the following morning. She also had to order stock every week.
I was able to access a computer every other day or so in the US so could answer any hard queries.
Considering I was having as many as 30 orders on some days, she did an absolutely fantastic job. I took a few days before I went to show her how to do everything and let her man the fort for the couple of days before I went so we could check she was ok with everything.
She actually enjoyed it, and although it was only 5 weeks, she learnt a lot about business - a quick response to an e-mail leads to a sale or re assures a customer and she was thrilled to receive e-mails from customers thanking her for prompt service and found it hilarious that people would send things to the 'Returns Department' when it was just a 14 year old girl in a bedroom.
And before anyone asks - I didn't pay her (i felt I was pushing on illegal due to her age and didn't want any tax implications, or child labour!), but bought her back a really nice present which she appreciated.
To answer the OP, I would entrust a family member again as long as they are happy to do it. The other thing I have done is arrange with my supplier to do a temporary drop shipping service. Was ok for a couple of weeks, but I still had to answer e-mails which annoyed my girlfriend somewhat as I couldn't truly 'holiday'. That is, of course, one of the downsides of being self employed - holidays are hard to come by.