I sense that you are more worried about your job, I know thats the case for me. My kids get sick and they need me and I am good with that, but I worry about not being at work and getting fired etc. Its ok to feel this way first of all. Its not horrible! You are putting the correct things in priority by being home. Feel good about that. Its good also to have a good work ethic!
Most of the time I personally am over reacting! My boss has been great and he has kids of his own so he understands. I give it to him straight, especially if its more than a cold. Also, you are entitled to caring for you children by law and they can't fire you! So rest your mind at ease there.
Tell them up front when your child is sick. Try to be accomidating to make doctors appointments all on the same day so you miss a whole day instead of a couple hours here and there.
Tell your boss you feel bad about missing work. Let him know you can work from home, if you think you will have time. Take some work home with you maybe. If you ask the technical part of your organization I bet you can get email from home on the internet and maybe even remote control your computer from home too!
My company does both email and remote control of the computer but I had to really ask alot to get it set up. It really saves me sometimes!
Good luck!