Your brother-in-law died less than two months ago. Your husband is probably still grieving and needs time to heal. If he has trouble resolving his grief issues after a reasonable amount of time, then speaking to a grief counselor could help. In the meantime, your love and understanding will go a long way. Losing your brother-in-law like that would do anybody a world of hurt. I disagree with the suggestion above that he should be taking antidepressants. That is not something people just move past in a couple of weeks, and what he is going through may be perfectly reasonable. Drugging himself up will not automatically help him.
It couldn't hurt to talk to his Bishop if he has a good relationship with him and this particular Bishop is the right person to speak to. However, I have noticed that Mormons can blend the line between spiritual counselor and psychological counselor. Bishops are often asked to give counsel on matters that they do not have any training for. If your husband needs help with his grieving process, there are grief counselors out there who are specifically educated to help with this sort of problem.
I completely agree with what FairChild said about your sister's actions. Your sister's children need to see that their aunt is focusing on loving them and helping them heal from this horrible event. I don't see how it could help to prioritize her messy relationship choices over their healing process.