Something which stands out about the existing ones is that they are not overtly sexual and they're symbolic rather than a depiction of the partner. The "paw" usually is a paw print, the horseshoe isn't even a natural part of the animal's life and the Queen of Spades requires like 2-3 distinct racist stereotypes to explain properly.
In light of this for spiders it's pretty obvious: the typical web icon, and a heart in the middle/around it for the more risqué version.
For other arthropods it really depends on the subset a particular person focuses on and the other sexual themes at play. Since you mentioned breeding one fairly generic option might be a clutch of eggs, for ants it might be a crown with 6 legs coming out of it or the like. Basically something which does not show most of an animal's body, and could be talked out of via some "artistic" interpretation as not pertaining to sex. Pretty much the exact opposite of the fly-on-brackets example above, that one would be part of body graffiti for exhibitionist or degradation purposes not a symbol of allegiance.
