Well there are a few assumptions in that. I don't agree that Leia would easily sense Rey is her daughter. Maybe she thought her daughter or Luke's daughter was killed like everyone else? Vader was not able to sense Leia was his despite having a lot more time with her. Vader is far more force sensitive than Leia too, and was in the same room while Leia was being tortured, yet he had no clue Leia was his daughter. How would Leia, who is far less force sensitive, know that Rey is her kid from a few quick meetings? Of course she can sense Han's death - she has spent the better part of her life with him, so I would expect her minimal force abilities to pick up on the death of her soulmate and/or the decent of her son towards the dark side in the same moment.
I'm also not sure Leia "sends" Rey to go get Skywalker. They may have agreed on that approach, but do we ever hear that Chewie or Rey (or the Falcon) are part of Leia's Resistance group? Whether she is related to the Skywalkers or Solos, I would want her to go find Luke because she's the only other light side force user they know of. If Luke wanted to continue to stay hidden, he'd probably have a good chance of doing so unless the person looking could sense him in the force. Leia doesn't sound like she can do much with the force and is probably needed elsewhere, so Rey just makes the most sense, especially since she has Luke's saber, needs training, and may or may not be related.