Kim Kardashian is mulling over a big decision ... whether to go to court and ask a judge to strip Kanye West of joint legal custody of their 4 kids, because her ex-husband has flagrantly ignored their custody agreement.

The latest legal war was set off after Kanye agreed in a mediation Friday not to release a previously recorded song in which their daughter North raps. The track -- "Lonely Roads Still Go to Sunshine" -- also includes a phone convo between Diddy and Kanye.

Thing is ... Kim was vehemently opposed to letting North participate in any way ... and according to their divorce settlement, they both have equal say in making decisions for their kids.

Sources with direct knowledge tell TMZ, the divorce settlement provides for the event there's a conflict -- Kim and Kanye must first go to a private judge to try and hash out an agreement. Kim was there for the mediation with her lawyer, Disso Queen Laura Wasser, and his lawyer, Patrick DeCarolis, and they did reach an agreement ... North would not appear on any version of the song if it was released.

But agreements don't seem to matter with Kanye, and he released the song with North's voice over the weekend. Kanye posted to X last night ... "THE MAN MAKES THE FINAL DECISION."

So, here's what Kim is weighing ... Kanye rarely sees his kids, so physical custody is not an issue. In fact, Kim wants their kids to have a relationship with their dad and has almost always facilitated that. One recent exception ... when Kanye held an event where he urged participants to wear swastika shirts. She did not feel it was appropriate for her kids to attend that event.

As for legal custody, he's not that involved in decision-making, but still -- Kanye has made it clear he's not about to follow the rules of the road. So our sources say Kim is seriously considering going to court to ask a judge to strip him of joint legal custody.