From the perspective of a teacher and a parent of little ones, I say that school should be a fun and exciting activity for your child. It is important that they not see mom or dad sad, even jokingly, to see them go to school. Keep it lighthearted so that they aren't torn between home and school. If you think about it, it isn't really fair to put them in the position of feeling that they are hurting you in any way. If you need to shed some tears, try to save them for the car or another "coping" parent's shoulder!
How to "cope":
1. First of all, stop saying "cope"! You have done a great job preparing your child for school so now's the time to step into a new parenting role, sharing some of the job of educating your child with some very special people, teachers! It's not about coping - this isn't a tragedy - it's about being thrilled that you've made it this far and that you've given your child the skills to take on this new challenge! What an accomplishment, nurturing a tiny and helpless newborn to becoming a incredible walking/talking/thinking/feeling little person on his/her way to great things! Sure, the thought makes tears well up in my eyes too, but this truly is a momentous occasion to be celebrated.
2. Make it about you! Now that you have a few hours of free time, don't waste it! Make this your special time - do what you've been putting off during the long years with little ones at home fulltime - get some exercise, work part-time or rededicate yourself to standing out a bit more at work, start that at-home business, do some shopping or remodeling, take a class, take up or return to a long-lost hobby, meet up with friends without having it be a playdate or storytime! Or just relax! You've earned it!
3. Volunteer! If you really can't part with your child, stay close by volunteering at the school. I wouldn't volunteer regularly in your own child's class simply because it can make it difficult for the child to see themselves as capable of "surviving" without you and it is tempting for parents to overanalyze what is going on in the class. Allow your child this space to make their own way in this new world, make new friends, and develop new bonds with their teachers without your guidance. This is an empowering moment for your child. You'll feel closer to your child just by being in the loop, working with teachers and administrators, taking on projects, helping out at school events, and so on. Volunteering will give you a sense of purpose and accomplishment as well.
4. Focus on your own goals. Now that schooling has begun, the time you spend on your own away from your child will only grow, as hard as that is to face. I have a kindergartner and I wonder how I'll "cope" when he goes full-day next year. So let's take this time to make out a five-year or an even longer plan. Do you want to go back to school? Are you working and need additional certification or coursework? Do you want to have more children? Do you want to start a business? Where do you see yourself when your child is in school fulltime? Planning now will help you avoid the emptiness that is sure to come when that happens.
Remember that life is about stages - we have to pass through them no matter how painful they are or how long we try to avoid passing on to the next phase. This is spoken by someone who dragged her feet on every change with her firstborn only to see that the time comes to move on no matter what you do or how hard you fight it! With my second, I see things progressing even faster since she has a role model in her brother. I have chosen to let her move on at her own pace rather than pushing her to hang on to babyhood a bit longer for my sake! It's only fair.
Rather than struggling against change, accept and embrace it as a new opportunity for you and your child. Look at school as a source of fun new things you can be involved in with your child -field trips, projects, homework, sports, new friends, class parties, school events - school will just add another fascinating dimension to your relationship with your child and with yourself! Enjoy!