As you have a good job as a government employee, if you do apply to come to the UK on your own without your children and you got a letter from your school saying you are expected to return to work on a certain date, that would work in your favour. What might also work in your favour is that the ECO would know that you will have 2 kids at home in the Philippines waiting for you to return.
Do you have your own house there in the Philippines? If you do that would also work in your favour, it would be another reason to make the ECO think that you would be likely to return before your visa expires.
Iain.
