Is there a name for this or is it just Cuckolding backwards?

So, basically my and my gf are having a hella bdsm relationship. Not 24/7, but it’s for the most part a constant master/slave, daddy/baby, you name it.

We’re both experimentalists and exhibitionists, so we’re into cucking others. Basically, fuck while another guy/girl gets off from it.

Recently, we’ve been thinking of threesomes and such. A common uh, theme?, in our convos about it is, in short, pity fucking. As in, i tell her to fuck someone because they can’t find a girl cuz of dick size, or whatever. I’ve been wondering ever since, is there a name for this “fetish”. Is it even a fetish?

To me, it’s not me getting cucked, because i’ll always be in control, Plus, she always begs for me when we roleplay it (Yes we roleplay situations to test the waters). So yea, I was wondering uwu.

Sorry for any grammatical errors btw, English isn’t my best.

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