Can the grandparents try to get custody, if both parents (neglectful) live with the children in the grandparents home?

It is possible for grandparents to gain custody of their grandchildren; however it can be very difficult. Biological parents have a constitutional right to parent their children. This right can be terminated if the Court feels the parents are unfit. Grandparents do not have standing to petition the Court for custody of grandchildren unless both biological parents have been deemed unfit by the Court. I would contact an experienced local attorney and get the ball rolling soon if this is something you wish to do. Unfortunately, this process can take a while.

I agree with the previous answer, but would add that, based on what you're saying, you absolutely have standing to seek custody of your grandchildren. Having said that, there is no guarantee you will be successful because it is difficult to obtain custody against a biological parent. If the children's parents simply live with you, that is likely not enough to be successful without more indication that the parents have relinquished a substantial degree of parenting responsibilities.

Hope this helps-good luck!