I'm in agreement with most of the moms here... be more afraid of getting induced! There are so many problems with getting induced and all the interventions it often leads to. I know you said you were induced with your first, but by doing so, without medical need, you're putting your baby at much higher risk of SO MANY things. It may be more convenient for you, but just think of the consequences if baby isn't ready! Then you'll REALLY be inconvenienced.
Besides, babies aren't about convenience...
My second child came totally naturally (my first came when she was ready too, but I had an epidural, episiotomy and vacuum assistance) and was actually more convenient as she came. My husband had LOTS of things going on around the time of my due date (school for his master's degree, military obligations, and 2 jobs) and our little one decided to unearth herself on the day when he only had one thing to call and cancel on, and that was the military thing. It worked out nicely because my labor started in the morning and he wasn't leaving for his prior engagement until after lunch time. I told him around 11am that he wouldn't be going anywhere... It was a very easy labor, everything lasted about 6 hours and I was very relaxed, only had to push for about 5 minutes. What a great experience. But then... I wanted a natural labor!
Besides, most labors don't just happen in an instant like everyone who hasn't had a baby seems to think. Most likely you'll be wondering for a while "is this actual labor?"... and eventually it will become apparent. You'll probably have time to make arrangements. Just make a plan and let people know of your intentions. Everything will work out fine. Your first child will be fine making a last minute trip to grandma's or the neighbor's house for a day or so. Birthdays happen every day.