It sounds like you are on the right track to making a good decision. As you know, no birth is 100% guaranteed to go as planned. And your considerations for your partner/husband are smart--our partners can't fully be in both the support and caregiving roles.
One idea would be to have the sitter stay at your home with your daughter. However, some women are sensitive to having others around during their labor, so it all depends on your comfort level with this person.
I'm not sure, at 22 months, that she will have positive or unhappy memories of this time. It all depends on the child, and how your labor progresses. Some women have fairly uneventful labors and are able to stay centered, birthing relatively calmly ( I don't mean passive here--I mean no "freak out", screaming and shouting, etc.) . Others have a hard time managing their pain or might find a child's presence distracting.
I had a pretty staightforward home birth and can say that, if we were having a second child, my oldest would likely stay with a friend until the baby was born, and then we'd love to have him come right in when things like placenta, stitches and a shower had happened. But that's just me. I think his presence would be a distraction for me, and I know that he'd want to be with me. (Kiddo is a mom-seeking missile!) I don't believe that this would be a memory that would last him forever...but taking a picture with baby and big sibling on the first day would be a happy, tangible reminder of the day they became a big brother, or in your case, a big sister.
Best to you, whatever you choose.