Can a family have rights against an estate of a deceased loved one when they die from cancer having a will made up 6 weeks before they died

You can always challenge a will on the basis of undue influence.  That means that someone exerted such force on your loved one that it subverted their will, that it caused them to change their testamentary intent.  Usually the natural objects of someone's affection are their family members.  If they have left their estate to someone else, that is considered "unnatural" and may be the basis of a challenge.  The other way to challenge a will is to say the person lacked testamentary capacity - meaning they were not cognizant enough to make a will.  Good luck.  If you think this is something you need assistance with, feel free to call my office for a consultation.