Wife's sister's daughter to visit uk with wife's mother

I think it would be very difficult to get a UK visa for a 15 years old, as they would see it she has many working years ahead of her and could very easily disappear into the off the books jobs black market.

Have a look at PSAHelpline.ph which gives details of how to apply for a minor child's Philippine Passport. There are lots of requirements and they depend on individual circumstance but it does seem to cover everything including if the minor is travelling without their parents. You will need documentation from the minors mother and documents will need to be authenticated. Pay particular attention to the information listed for Minor applicants who are not accompanied by parent/parents during the passport application and also the section about Minors not travelling with parent/parents.

My biggest fear for you would be if you managed to get the passports for both, visas and all other documentation required and then your wife's mother or the  minor or both were pulled at the airport for interview and immigration insisted on contacting the minors mother in Saudi to clarify some points. You may end up loosing a lot of cash.

I do not think this is an easy task and it may be slightly easier if the minors mother could also make the trip with you all. That would obviously depend on personal circumstances. So do you need to make the trip before the mother of the child finishes her contract in Saudi?

PSA website is good 😊