I'm going to play devil's advocate, just so you have some things to think about that's not one-sided.
1) Separation issues are pretty normal for kids their ages. If you quit teaching because of that, the separation thing may just switch to another venue - dropping them off in the church nursery each Sunday, for instance, or date night.
2) You say you no longer need to work now that your husband has a better job, but what if that doesn't pan out? What if you have to go back to teaching? Will it look more professional to quit now, or wait until the end of the year? You will need to be able to give a compelling reason to a future employer for leaving your job mid-year. Is age-appropriate separation anxiety, or wanting to be home with my kids, compelling enough?
3) Yes it is very important to be an available parent and make the children God gave you a priority. However, our children should not the center of our universes. That's Jesus. What is Jesus calling you to do?
Now, of course, one woman's calling may be to not work so she can more fully focus on her children. Another woman's calling may be to work while also focusing on her children. And when a person is called to something, sometimes that something starts immediately, and sometimes it starts later as certain things need to be in place before the something can start.
As a mother of teens who has alternately worked and stayed home at different points in raising them, I can say that I highly doubt that your kids will be damaged if you wait 6 months to the end of the school year. It sounds to me like you are looking for justification to leave because you simply want to leave and be home with your kids, and you want it so much you want it to happen right away. You need to make sure that desire is from God, not from yourself.
From personal experience, I know that is not always easy to determine, so I feel for you. And I wrote all this not to convince you that you need to stay until the end of the school year, but to counter the premise I sometimes see in christian circles that a "good" christian mother doesn't work, period, if she doesn't have to. If God calls you to quit in December, how awesome and by all means do that. If God calls you to complete your commitment, he'll make sure it all works out.
I pray that God makes his will clear to you.