I am sorry your father is feeling poorly. This time must be very hard for your family.
I am not from the New Jersey area, so regretfully do not have any recommendations regarding care providers. I did look into hospice options in my own area some time ago, and found the following information which possibly might be helpful.
There seemed to be a county-affiliated office that advised on hospice care, with a focus on care provided in the home. I had the impression that hospice care in the home is the most usual situation. There was one actual hospice care center that looked positive to me. And a number of the care facilities for seniors indicated on their websites they could provide hospice care to their residents. This seemed to mean the family member could be given basic care in the facility, with visiting hospice services arranged to travel there, instead of to the home.
A lot depends these days on what insurance will cover. Please be aware that home hospice care does assume family members will provide some of the care under the guidance of the hospice medical providers. Families should be sure they know what that will entail, to make necessary arrangements. For example, if the family member might need to be assisted in moving around the house, the family would need to be sure to have the equipment and persons available to help with that.
I wish I had more help to offer. Your father is blessed to have his family supporting him, and I hope you can identify professional resources in your area.
Take care, regards, Mary