If there is a dependency case already going on, then it is too late. The juvenile court has "original jurisdiction" in a dependency case which means that a court could not grant your mom's request for 3rd party custody. If there was only a Voluntary Placement Agreement, then you could.
Because there is a dependency, you can still get your mom involved but it has to be through DCFS (the larger agency that CPS is part of) or the GAL. Your mom needs to submit her name, date of birth and social security in a letter requesting to be considered as a placement resource for the child(ren). Make 3 copies of the letter. Send one copy to the GAL (name of GAL, Pierce County Juvenile Court, 5501 Sixth Avenue, Tacoma WA 98406). Take the original and a copy to DCFS and give the original letter to the receptionist for the social worker. Have the receptionist stamp your copy because that is the only way you can prove that DCFS received the original letter. Keep the stamped copy for your records. Take the 3rd copy of the letter and send it to your defense attorney.
DCFS is required to seek family placement. You do not have veto power of which family placement they select. If you have substantive concerns about the sister, spell them out exactly. Be aware that DCFS may not be free to place with your mom. If your mom has a CPS history, criminal history or her home doesn't meet the guidelines for placement she will be turned down. Also, if the kids are school age and moving them to your mom means changing schools, you can be sure that it won't happen anytime in the next few months. There are lots of reasons why DCFS chooses placement with one person over another. One other issue that may come into play is your desire just to get CPS out of your life. If you are trying to get your mom custody to get out from under DCFS/CPS, then there would be concerns about whether your mom would really be in charge or whether you and your partner would run roughshod over her because the 3rd party custody is just a sham.
The best, but most time-consuming, method is to work with the social worker and the GAL to get them to agree on your mom as being the better placement.
I agree--if, that is, there has already been an adjudication of dependency. If, however, the child has not yet been adjudicated, you might be able to offer your mother as an alternative. Once the child is adjudicated dependent, there's no incentive for the State to backtrack and go the route of 3d party custody (i.e., they've already gotten it via the court).