My kids are 11, 8 and nearly 2, so similar ages to yours. I also would be happy for the older two to be away for 9 days but not my youngest.
When my eldest (and at the time, only) was 20 months dh and I went to Italy for a wedding and left ds with my aunt and uncle. We were away for 5 days and he had a wonderful time, as I knew he would. I had complete faith in my aunt, otherwise I wouldn't have left him. (My mum was 12 years older than my aunt, and my aunt lived with us when she was a teenager at university, so we had a very close relationship). However, 5 days was more than enough. I actually don't think I would leave my youngest for that length of time though, as she is a different child with different needs. Also, we haven't left her overnight with anyone because she doesn't sleep well.
I think you need to be realistic about what both you and your baby can handle in terms of separation, and ignore comments like 'overprotective'. It's your job to be protective, you know your kids best (especially the baby if you've been a single parent for most of her life) and you have to make practical and realistic choices.
Why don't you suggest he starts with a long weekend and take it from there. If necessary, get her dad to pay for you to fly out and come and get her, and let the older two stay a bit longer.
"If you really, really don't want a baby to make any difference, you could try not having one." Penelope Leach