I think there should be a new option called "investigate if real child"
But... how exactly? I mean, is not like you could take the child to a clinic and run a test. At most you would be able to look to the child intenselly and say: "Hm... his lower lips are not very Bourbon'esque" or whatever dynasty you are in, and that would make for some weak case at court unless your dynasty had being ruled by people with the "inbred" trait for quite a few generations or if they were marrying first cousins a lot over the years like the houses of Bourbon and Habsburg. But for all I know, even they only got to THAT point (to the pouting Bourbon mouth and the nightmarish Habsburg chin) mostly later, after the end of CK II's timeframe. And I'm almost sure the game wouldn't be able to cover that many variables.
or "investigate if spouse is cheating"
Now, that one would make a lot of sense as an intrigue option, specially for someone with an Intrigue focus. But than, again, for all fairness, that should probably have a chance of backfiring spectacularly. Bad information or a flat out lie coming out of it, a "maybe, maybe not" as an answer, rivalry and loss of both prestige and piety if proven wrong in his/her suspicions, perhaps making the investigated imune to further inquires for some time after a failure... otherwise, it would be a "take your time and you will know the unknowable" button, and people got VERY upset when Seduction played that sure-shotly.
if a child turns out to be a bastard, this should automatically disinherit them from any titles.
You are right but, technically, your character never discovered that the child is not hers, you did, so not really in this particular case. Nevertheless, since you used a cheat already to find the father, you can add_trait bastard and there it is.
P.s.: admiting your heir is a bastard should probably also incur in quite the drop in prestige for you, for all the bawdy jokes and gossips that would came with it.
