But if she's really concerned, then I do think it's more a matter of having a conversation about the harsh "you're going to kill your baby" judginess, because that is where the lie spawned from.
This, x10000. I think you should, as PPs suggested, invite him over for tea with your husband there, sit him down and break the news. You might also want to print out some information about homebirthing for him to read, or even give him your doctor/midwife's e-mail address - maybe talking to a medical professional about this will help educate him. But before you break the news, make sure he knows exactly why things are happening this way:
"FIL, I have to tell you something. The fact is, that I lied to you. The reason I did so was because I feel *whatever* when you talk about my baby being threatened. I have done the research, I am educated, I am smart, and I will never do anything to hurt my baby. You need to believe that, because if you don't believe that, it's incredibly hurtful and insulting to me. And when you make comments that show you believe that, I feel *fill in the blank*.
Because of all of that, I lied about where I am having my baby. This will be a homebirth, with an experienced midwife. This is not up for debate, and I will not listen to your judgements about it. I love you, I'm thrilled your a part of our lives, but my birthing choice is my choice and I need you to accept it."
Make sure he knows that his behaviour is unacceptable in pushing hospitalization when you've made a different choice.