Hi T.,
First of all, what your wife is going through is EXTREMELY normal. Braxton-Hicks are the way the uterus prepares and strengthens itself for labor. They may feel strong now, but they are very different from real contractions and believe me, your wife will know the difference!
Secondly, with regards to due dates, due dates are NOT an absolute. In particular, with first time labors, many women will naturally go to 42 weeks and sometimes a little beyond, with no harm or detriment to the baby or the mom. It's better and safer for both baby and mom if you wait for baby to come. Scheduling an induction can lead to significant labor risks which can lead to increased morbidity and mortality.
With the water breaking: There's no such thing as breaking in time for labor. With my first child, my water broke 40 hours into labor. With my second and third, my water broke as my children were being delivered. (Artificially rupturing membranes can lead to complications which can again cause problems for mother and baby.)
The last month of pregnancy, honestly, hurts a lot. Nothing like giving birth, but it's grossly uncomfortable, and it is what it is. My mother told me that the ninth month of pregnancy was god's way of making a woman want to go through labor. That always made me laugh, because it's totally true!
Be with her. Support her. Rub her back and her feet. Don't let her get over-exerted. Make sure she eats lots of high-protein foods, and drink PLENTY of water. Keep her in the air conditioning (August is a miserable month to be nine months pregnant in, been there, done that!)
Your baby will come soon enough :-)