I'm not Filipino but this question is fascinating because the mano is really similar to hand-kissing or "salam" in the Malay culture. In both you use your right hand, do it when you see your elders and it's a sign of respect. I still salam my elders and I think it's important to keep the tradition when I have kids. I will definitely teach them and you should too. It's ok to hug and have Western greetings but at the end of the day, I find that Asians have soooo many unique ways of showing respect, it'll be a waste not to preserve them :)
Magbasa pa