Recommendations for 11 and 9 year old daughters

Ratchet and Clank

Lego Dimensions. All 3 of them will love it.

If you don't want to go the toys to life route, get pretty much any Lego game. They are all awesome and are good for all ages. Some of the earlier ones have no voice acting, so I would be aware of that if it is a hang up for your family. None of the new Lego titles are that way. I think they started using voice actors with Lego Batman 2, but it may have been before that.

ETA: I love all the Lego games and play Dimensions with my 9 year old daughter every chance we get.

Get Inside. Great game. Absolutely no dialogue. It has an open-ended narrative; you kind of use your imagination to understand what the heck is happening. My daughter is a bit older, but she loved it. We went back and forth about what the story was really about.

Little Big Planet was ok. There is Minecraft for the PS4, too. Knack is good for kids. I would recommend the first Tomb Raider (2013), but that may be a little too violent for your tastes. But, the main character is a badass young woman. Rocket League, but I don't know if you allow online gaming and I don't know if the community is full of people cussing and talking smack like other sports/shooter games. Mirror's Edge is listed as 16 and up, but features a female protagonist.

My daughter's favorite back when it came out (she was 10), even though there's a lot of cussing in it, was TLOU. She made me play it because it scared her, but she just *had* to follow the story. Obviously I didn't like the cussing, but I was there and we kept talking about the story and characters. Discussions about what we'd do in the situations the game presented. She cried a lot But I wouldn't recommend it for them to play alone.