You should spend time hanging out with her and her family.
Either inside the house or going out somewhere. Being with them always
makes them know more about you also. They will become comfortable with
you around and probably earn their trust on you.
They might challenge you to a game her dad likes, make you help
plant on her mom's backyard, or even make you drive the whole family to
just anywhere they like. If you'll be able to pass these things and see
you as the right man for their girl, they will be in favor of
you. Fortunately, the family will be advising or push their girl
to like you the way they like you.
Just remember that Filipinas love to be showered
with attention from their partners. Respect is always important too.
Understanding her and making her important people important for you is
also a must. You should always remember that "Pinays" just like any
other girls in the world, They needed your unconditional
"LOVE"