Well, you don't have any legal entitlement and no financial obligation but if you and the kids were close then you certainly were a "Dad" to them (kids can have more than one). Hopefully they will cherish that relationship in the future despite their mother's objection.
Fortunately, it won't be long until they become adults and make there own decisions about a relationship with you.
Meantime, don't make an issue of it. After the divorce you might be able to make some inroads once the dust settles.