I think that is a great idea!
and your family should definatly understand!
popping out a baby is no easy feat - and with bub number 2 you are going to need all the rest you can get!!!!
You can also let the midwives know that you dont want to many visitors and you dont want them there for long also! they are usually pretty good with that!
I had a big massive influx of visitors one afternoon after i had just managed to get Bianca settled with the help of a couple of midvives and when they all arrived i didnt want to tell them they couldnt pick her up for a cuddle - so the midwife did it for me! she was great - she looked like the meanie not me! but it worked no one picked her up and all were very quiet and didnt stay long!
Let us know how u go with the email! but dont worry too much - all will be fine!