Does the termination of cohabitation between live-in partners simply physical separation (ayawan na)?

Would this terminate the marital obligations even if both partners have common children?

in the first place neither of the two has marital obligations; because they are not legally married...
they might be engage for so long as though legal couple with kids, but if they did not execute any affidavit of cohabitation or been married, neither of them has marital obligations...

There might no obligation to support financially the wife..but the obligation to the childrens will nit cease

I think I agree that support between spouses will stop but to children, both parents are required under FC to extend support. Source: #1 - separate property; #2 - conjugal properties, of subsequent marriage but treated as advances of one's share.