Firstly do the children have passports? If they don't the first thing you must do is get them some as they can't be issued with visas if they don't even have passports.
It's quite difficult to apply for visas from this end because the applications must be made to the British Embassy in the Philippines. In our case we downloaded the settlement visa form and filled it in, then compiled all of the evidence required, ie salary slips, bank/savings/mortgage statements, letters of support, accomodation info, evidence of relationship, financial support and regular contact.
Up to that point things are relatively simple. Then you have to send money and get someone in the Philippines to get you a managers cheque for the visa fee made out to the British Embassy Manila and drawn on a Philippine bank (we used the PNB). Then they must send it to you by a reliable courier such as DHL. When they send it they should put it in an A4 envelope amongst lots of blank sheets of A4 and tell the courier company that it contains documents...... if they tell them that it contains a cheque they will refuse to carry it.
Once you get the cheque (which should be within 2 of weeks of it being issued as it may only be valid for a month) you just add it to the completed application pack and send it by courier (we used Interparcel http://www.interparcel.com ) to the British Embassy in Manila.
You should find out the exact fee and include the courier fee for them to return the application pack when the visas have been issued, otherwise it will have to collected from Manila....... The application pack will be returned to the address of the applicants, ie the children, not to your wife in the UK.
Just to make sure that all that I have told you is still relevant today, If I were you I would send an email to the British Embassy in Manila using the following address as they usually reply to to emails addressed to here with a week or so: ManilaVisaEnquiries.Manila@fco.gov.uk , I would give the email the subject "Making a visa application from the UK to Manila".
Iain.