Wow this is a really hard one! I was sort of in the same boat, but my family came over from so 20 hours away and had never been to Australia before! Initially I really wanted them to be there ASAP after the birth as I wanted them to share it with us, but I was really worried about everyone coming for the due date and then sitting around waiting for me to go into labour... nightmare! I assumed that I would go overdue as first baby so was scared too that they would only have a few days with him before having to go back if I went 10 days/2 weeks overdue. So anyway after much deliberation they all booked to arrive 3 days after due date. I actually delivered a week early so we had a full 10 days just us with no family and it was wonderful. We were so shellshocked and had time to recover and get to know him without having to worry about anyone else. I can't actually imagine having them around that early now, it worked out perfectly... and a baby at 10 days old is pretty much the same as 1 day old so I don't feel that they missed out on anything!! We too had a tiny house so they rented a house 2 streets away- expensive but SO much better as we had time by ourselves... but on the flipside the tricky times in the evenings when we were trying to settle him we were mostly on our own. It would have been nice to have them around a bit more than we did in retrospect, but I was sick with mastitis and it was tricky juggling all the family.

So anyway, I think you have the right idea, ask them to come a bit after you expect to deliver... unfortunately that's a bit tricky to know! You could go early or late! It is definitely important to have some time to find your feet without someone looking over your shoulder imo... but then if they're not staying you can ask them for some space anyway if you need it.

Good luck and hope it works out ok!