Father of my children threats to sue me if i bring them to study abroad.

Dear Atty. ,

Good day!

I would like to post a concern regarding my situation with my kids.I conceived my daughters eldest 8 and the second 7, from their father not being married to him but have his last name in both their birth certificates. When I went abroad I heard things from my family bringing his other women in the apartment which i used to pay  while I work abroad (were in my own father and kids are in the my apartment), and sending the kids with their nanny out to the playground at 2PM while they are inside the masters bedroom and my father in the living room. That provoked me to separate him ( this incident happened way back 2009). now for almost 2 years he is not giving any financial support to the kids even just an allowance for their school or anything (which is very fine with me) ,  since i was the one paying for their tuition fees and all there wants and needs with the help of my mom ever since. Currently i am now with someone which we now have a daughter together, he is so responsible and helping me care for my daughters and helping me support them and not at all interfering with their fathers right to visit or borrow them which my x doesn’t do at all. we are working now abroad and we are planning to go for vacation and bring the 3 kids with us to study here but not to migrate since we are in a country that doesn't have migrants. P.S. I was never rude, I am very understanding I am even friends with the live-in partner of my x and specially with him, and she one time out of the blues sent me a message that she is pushing the father of the kids to visit them but he never comes, even during Christmas, new year’s, their birthdays specially there 7th bdays nothing at all even to greet them or to have them hear from him nothing which in one point I thought he might have died already... I informed her ( the live- in partner)that i am planning to bring the kids here so at least to grow with one of their parents beside them ,( cause having him in the Philippines near to them makes no difference of me being thousand miles away from the kids, but the difference is that I never lack of any attention and love a parent can give and they never felt alone since I am always there for them even if physically absent ), And if he sees them it is because he was forced by his live in partner. His live in partner told me about his very horrible attitude to the point one day he got very jealous and strangled her, and she said he won’t allow the kids to travel abroad and sue me to court.. Pls. PLs. help me what’s the best thing i should do and be reminded of my rights specially in having them travel with me??

Thank you and God's speed.