Everyone grieves differently and to tell anyone that they are grieving wrong will probably just drive a nice huge wedge in between you and them. Instead, tell your mom that it is extremely difficult for you and express your emotions bluntly. Tell your sister that it is normal for mom to want to find another man to cling to for comfort but that you don't agree. But don't tell her this isn't "normal". It may be too soon for you, but don't expect mom to grieve at your pace. A wife has a different relationship than a daughter and it may very well be harder on you. Just know that you are grieving and these feelings ARE normal. Very normal. When my son died, I heard many people telling me how to grieve. I really needed to do it my way in order to heal though. When my best friend was murdered, I was told it wasn't appropriate to party in her name. But I did it anyway and I felt better for it. Grief is very different for us all. You need to grieve at your pace, but it may not be the same pace as your mom, just don't punish her for it.

You know I want her to be happy. I just don't want her to be so secrative about it. It kills me that she will no longer return my phone calls, and
when I ask her who she is talk to, she will not answer me. Or if she does answer me, she says that it is just a friend. My sister is 17. My mom is staying out all hours of the night with my little sister home alone. I am not trying to punish her for it. I have even told her that I want her to be happy, I just want to know who she seeing. I am her daughter. This breaks my heart to know that she does not want us to be apart of the new relationship.

It may not even be a relationship at all. This just may be a person that is giving her comfort, but maybe deep down that's all it is. So that may be why she is not involving her children. Also, she can sense and see that you are not happy with he choices, so maybe that's why she is not involving you as well. Everyone grieves differently. To some it is a wrong thing to do. But how long were your parents married? She may be tremendously lonely and this is the only thing she knows how to do.
I have been a mother all my life. I had kids really really young. I'm a mom, that's my job. Now my son, who was sick is gone and I was supposed to take care of him the rest of my life. My girls are almost done with school and on their way to move out in a short couple of years. Now I want a baby so bad because I feel so alone, I am a mom, that's all I know how to do.
Maybe it might be the same thing for your mom. She is a wife and that's all she knows to do?