Your question is asked based on the slightly incorrect assumption: Leia did not "send Han to save Kylo Ren", paraphrasing the question.
Han volunteered to take the
stolen Imperial shuttle Falcon and deliver the team to Endor Starkiller, to blow up/disable the shield generator for the Death StarStarkiller, so Rebel fighters Resistance X-Wings could attack and destroy the power source the oscillator.
Her asking him to save Kylo Ren was just a side-quest, in case he meets Kylo Ren.
Leaving THAT aside, it seems to be a really really bad idea to ...
... send away the main leader of the Resistance on a personal errand, when the New Republic just got Alderaaned, and First Order seems to be winning.
... send the main leader of the Resistance to a First Order stronghold where she'll be likely to be killed by FO.
... send the main leader of the Resistance to a First Order stronghold where she'll be likely to be captured, tortured, interrogated, and give up all the secret information about the Resistance, that she is a leader of.
... send the main leader of the Resistance to talk to a Dark Side user who's a main thug for First Order, and is more likely to kill her OR torture her for information, than to give her a warm hug. And unlike the rest of First Order, he can actually mind-read her, successfully, even if she's still as resistant to torture in her old dotage as she was when on board First Death Star.
... send a "Jedi" (or light force user, at least) to a Dark Force user, who would quite likely hate her for that far more than he hates Han.
Also, putting on my cynical hat, she has absolutely no use for Han at this point. She snaps and barks at him, gives a complete impression of hating his guts, and generally doesn't seem to be the type of a romantic partner (or in a type of romantic situation) where you would rather risk your own life than the other person's life.
Because of that, in ANY of the 3 outcomes, it's a win/win for Leia.
Han gets to be the canary in the mine, and 3 things can happen:
If Kylo Ren is in the Oedipal mood, expendable Han gets offed, and Leia knows not to step into the minefield. No big loss to her compared to status quo.
If Han isn't killed but doesn't succeed in talking KR down, Leia can always make a try next, when she's less busy; and play "good parent/bad parent" gambit.
If Han talks KR down, she gets what she wants (her son back, no apprentice for Snoke)