All non JW's are basically considered "bad associations" and they feel that having to do with non-JW's will in time lead to the spoiling of their "useful habits" - they think they'll will be 'tainted' by prolonged contact basically - so they limit or in some cases eliminate their association with non-JW's, including family members.
Yes, such behaviour is "Normal" for JW's. JW's are a cult, remember, so such behaviour is to be expected, unfortunately.
I think, if it upsets your family and you, that you should to communicate that you miss them in a really heartfelt manner. Perhaps such a thing will melt their icy and rather heartless attitude enough for them to stay in touch a bit. If not, then at least you know where you stand after that. But whatever the outcome, remember that it's not wholly their fault. They are instructed to act this way. They are not 'themselves', they are trying to be who they've been told and deceived into thinking they must be, to please God.
If they do resume contact, then perhaps, after educating yourself about the JW's and their teachings and history you might be in a position to very subtly, over time, help your family realize the error of the JW religion and you may end up unifying your family once again. But this would take time and a very delicate touch. Many people here can advise about this and would be glad to be of help.
One way you or a family member could do this would be to show an interest in the religion, perhaps even indicating you may want to 'study' it, but asking specific questions the answers to which your family will have to find through research and which will surprise them and will expose things about the JW Organization that were hidden from them and that they were deceived about. Thus, the 'study' is really for them, even though they thought it was for you, and you actually knew the answers to the questions you asked, although they did not. JW's are taught they and they alone have the answers to everything. They generally don't listen to anyone else, so it's very hard to teach them or tell them anything directly, it has to be done indirectly, with them imagining they are the ones teaching you.