This is not a process you should try to do youself. I would suggest you contact a family law attorney and get their advice as to how to accomplish your goals of good care and a stable home life for your granddaughter.
These type of cases do not have a simple answers and this forum is not a proper venue to obtain a complete answer.
This response is intended to be a general statement of law that should not be relied upon as legal advice and does not create an attorney/client relationship.
Under Missouri law, a parent is the natural guardian of their child. That said,Missouri law permits a non-parent to obtain guardianship of a minor child when the parents are unable, unwilling or unfit to perform their parental responsibilities. In order to overcome the presumption that parents are fit guardians. We are all entitled to adequate guardians, we are not necessarily entitled to good parents. As such, you will have to show specific and continuing acts by the parents that go beyond "questionable parenting".
As the other poster suggested, this is not an area to delve into without professional representation. A lot is at stake, including the welfare of your grand child, as well as your relationship with your daughter. If you charge into this sort of action without competent advice and careful consideration, you may alienate your daughter and risk never seeing your grandchild again. An attorney practicing in this field in your area will be able to assist you in evaluating the merits of your case and the likelihood of success. Given the sensitive nature of the case, you will get the most benefit from scheduling a face-to-face meeting with an attorney.
NOTICE: This response should not be relied upon as legal advice and does not create an attorney/client relationship. Absent a signed attorney/client fee agreement nothing I have said here should cause you to believe that I represent you in this or any other matter.