I know you are having a difficult time and perhaps you could go to the hospice grief group as well. I can understand that you feel you need to be strong for your dad but not to grieve is rather strong.
I think being vulnerable and both crying and hugging can be an incredible release as you both loved your mom so very much... tears are cleansing... and for you to keep a mask of strength is not really being authentic with yourself or your dad.. on one hand, you wanted your sister to be open and honest with you and you in fact are doing something similar with your dad, thinking he can't handle it.
Crying is not bad.. it cleanses the soul.. there is loss, there is pain, there is fear.. there are so many emotions that can arise for both of you.. making it safe for you to both express yourself is an incredible support for one another during this time of loss... please keep us posted... my thoughts and prayers are with you and your dad.
richest blessings and may your healing journeys be gentle and nurturing.