Can I still receive WA state istance if I live with my parents?

I am worried my eligibility for DSHS is in jeopardy because I live with my parents temporarily with my daughter. Her father and I split months ago and he has done/doing everything he can to hurt me, including not taking his own daughter (ever) so that Im "stuck" at home with her and cant do anything. I recived a letter in the mail from dshs saying a 3rd party informed them he was living with me. I was sure I had given them a different address but recieved it at my parents. DSHS is requesting proof if he does and if he doesnt. I know it was him who set this up and he also doesnt want to pay childsupport or any istance back. I can get the "proof" dshs needs but if I lie about living at parents he will find other ways to prove i lied and so on. Please help! Any supporting info to your answers will be greatly appreciated! I have so many other questions regarding this type of thing (custody, sepperation etc.) so if anyone is close by and is or has gone through what im going through I could really use someone to feed off of. Thanks