A little preparation can save you an awful lot of stress in moments like these, and I have some suggestions for you.
There are a few things you should always have at the ready, packed up and kept in the car in case of emergencies. Buy yourself an inexpensive tote bag and put these things in it:
o Extra diapers and baby wipes
o Hand sanitizer
o Extra clothes for your baby or child (two sets would be a good idea, one for warm weather, one for chilly)
o A few toiletries (hairbrush, nail clippers, nail file, tissues, hair detangler)
o A first-aid kit, which technically everyone should keep nearby, whether they have children or not
o A few baby blankets; sun block
o If you have a girl, extra hair things. (You know if you're heading out for a drive that lasts an hour or more, your daughter's hair is going to get a monstrous snarl in the back, right where she's been rubbing up against her car seat, and sometimes you need to improvise a quick hairdo, like a bun.)
Now, this isn't your diaper bag, remember. This is your emergency bag. Keep it well-stocked and leave it in your car. I promise it will serve you well.
Another good idea is keeping a "fun bag." If you know you're going to be doing something quiet and possibly lengthy, like sitting in a doctor's office, for instance, or going to church, this stash is going to be a life-saver.
Put in the fun bag things you know your child likes:
o A notebook to draw in and a box of crayons (not markers; why ask for trouble?)
o A puzzle
o A teething ring or two, if you have a baby.
o Don't be tempted to put in something that makes noise - you'll regret it like nothing else. Something that lights up would be fine, or a toy that vibrates.
Keep this little collection special, something your child or baby only gets to enjoy when you're out. Let them know that by being quiet they're earning this reward. Then these times will be something they look forward to.
One last thought: When you have an appointment, it's a good idea to get ready an hour earlier than you think you need to. Give yourself room for unexpected disasters. And above all else, make sure a bathroom run or diaper change is taken care of before you leave the house, else you'll be sure to hear "Mommy " a lot sooner than you want to.