ebis1231,
Yes it is conjugal property when the title states the "name of the owner, married to name of spouse."
Under the law of Succession, the property, rights and obligations to the extent of the value of the inheritance, of a person are transmitted through his death by his will or by operation of law.
Assuming there was no will executed by your mother, then what you should do next is to execute a Deed of Extrajudicial Settlement of the Estate of your mother. This is needed for the legal transfer of the properties to whomever in your family, depending on what you put in the Manner of Distribution in your Deed of Extrajudicial Settlement.
Take note though, that only the 1/2 conjugal share of your mother will be subject to the settlement. However, the half conjugal share of your father may be waived in the same document as well.
I suggest you consult the services of a lawyer. He will explain more on the specifics, since I can only explain here based on the information made available.
Hope you get the general idea though.