YADNBU not to want to hand your baby over to your SIL for a whole day, SchrodingersMew - If she wants to help, she can come over and do some cooking or cleaning for you, or cuddle the baby whilst you have a bath or shower.
Regarding the wedding - dh and I took ds1 to a wedding when he was about 10 months old (so similar age to what your baby will be next June), and it was actually fine. It was a very relaxed wedding, though, so we never felt stressed about his behaviour at the ceremony or the reception. I can imagine it would have been much more stressful if it had been a really full-on, formal wedding, or if ds1 had been being grabbed by the bride and groom for photos every few minutes.
If you want to put her off the wedding idea, you could tell her that by then, your baby will be weaning, and learning to feed himself, and that this will be an extremely messy business, and you'd hate for her wedding dress to get spoiled.
Regarding telling them if you are in labour, the fact that you have a set date to be induced does mean they will know that things are happening/about to start happening, so you might want to think about a way of making sure you and your dh are in control of the flow of information. You could tell them that your dh will phone one designated relative at certain, set intervals, and update them, and that all other relatives wanting info should phone the designated relative, and should NOT bother either you, your dh or the labour ward.
My PIL visited me during my first, very long labour, and it was fine - because they were sensitive to my needs, and I didn't feel imposed upon at all. Same applied to having them, and my dsis visit whilst ds1 and I were in hospital post partum (for a week, as he got neonatal jaundice) - from the sound of them, though, I'm not sure I'd have felt the same if I had your ILs.
You have to do what feels right for you. But if neccessary, perhaps we could create a human wall of mumsnetters, all telling your ILs 'NO!'