without knowing the exact reasons for refusal, but you do say that the embassy said your children don't need you're presence.

since 1998 you've not lived with your children?, I'll guess they refused the visa because you don't have 'sole responsibility' for them, and I'm guessing the embassy said who ever looks after your children has 'sole responsibility'

appealing doesn't cost anything but from what you've said it looks to me you don't have 'sole responsibility' , and you probably wouldn't win an appeal.

i think you'll be refused again for the same reasons, thou you should get (some free ) legal advice from your local law centre http://www.lawcentres.org.uk/directory/location/ or/and contact http://www.iasuk.org/home.aspx for some help

are you married to a brit ? and how old are your children ?
what type of visa do you have ? ilr / citizenship ?

maybe the only way you can get around this is to go back and live in the phils with your children for 6 months or a year hopefully that should be long enough to say you have 'sole responsibility' but seek legal advice..