I didn't have a home birth with my last but was in a tiny birthcentre with just us and the midwife there. I had my 10yo DD with us, she wanted to witness the birth. I wanted her to see birth as something good and doesn't always end in tragedy, as she was very aware and involved with my previous pregnancy so it hit her so hard when the twins died so I was happy for her to be there but we had a lot of discussions about it to make sure she knew what to expect and she could change her mind if she wanted. Before DS was born we watched a few youtube videos of homebirths together and discussed what was happening so she would know what was likely to happen, and she was well warned that I might make noises and that there would be blood. She was fascinated by it all and not grossed out at all, I was surprised. I also showed her how the babies don't come out pink and can be purple or blue, so she wouldn't panic and think he'd died. We actually just finished watching some clips when my waters popped, obviously DS decided his sister was prepared! I didn't tell her though as I didn't want her to get all hyped up too soon and my labour with her was 20+ hrs (ending in C/S but that's another story) so just doddled around getting things ready etc but things surprised me and ramped up pretty fast - this labour was only 4hrs, then about 2 pushing, but it was my body's first time pushing out a baby even though I'd laboured before and it wasn't full-on pushing for most of it. So second labours can definitely go a lot faster!
For what it's worth, she was a great help - even helping the midwife and took all our first pics etc and she was very quiet while I was labouring, which would have been hard for her as she's a motor mouth normally. She did say afterwards that she was a bit scared at one point, but it was fear he'd die - but that was just because we'd suffered a loss before, I don't think it was a normal reaction to birth at all, it's very common after loss, most kids wouldn't feel that way if they had no reason to.
She is very very bonded to DS, she is like a second wee Mum to him, I had to wrestle him off of her sometimes to change nappies and things as she wanted to do everything at first! She still loves playing with him and making him laugh and he loves her to bits, it's lovely. Poor wee boy won't get away with anything growing up with his 2 Mums though ha!
It was a very special time for us, even though I am a very private person and would maybe have laboured easier alone I pretty much zoned out anyway. We all stayed together in the room at the birth centre that night for the next couple of days, DH took her to the park for a bit and things and back together again so it was the closest we could get to a home-away-from-home birth.
Anyway, that's a very long-winded way of saying ask them and prepare them well if they do want to be there and they should be fine but maybe have a friend or someone they could go to if it all gets a bit too much or in the unlikely event you need transferred. You are also quite likely to labour at night so may want to just wake them toward the end if they do want to be part of it so they don't get bored or start to worry. For those of us doing the labouring time goes quite fast but not so much for those watching.
If I'm ever lucky enough to have a next time I think I'd rather stay at home and with a fast labour last time and a 3 hour journey to hospital it's probably the best and safest choice for me, it would be a different story with a toddler though but DD would no doubt lend a hand with him if it came to it. But I'm jumping away ahead, I'm not even pregnant
Sorry for the inconcise ramble, hope it helped a bit though xx
I think with most kids, you can just explain to them that mommy might make scary noises but that everything is okay.
