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You would need to breed the resulting foals with hom axiom red horses, for a 50/50 chance at either hom axiom red or het axiom red/het nexus. Unfortunately there is no guaranteed way to only get hom axiom red out of that foal, or any like her.

If you are trying to make a foal that is NrNr (like the dam), both parents need at least one copy of Axiom red, since the sire and dam each contribute one gene to the foal. Stallion The Magistrate only has hom Nexus NxNx, no Axiom, so he cannot ever contribute Axiom red.

Rumble and Red Mystery will always give you hom Axiom red NrNr foals, like your foal Mystery Rum, because they are both hom Axiom red.

If you don’t want your Magistrate x Red Mystery foal to go to waste, FallenShadows714 has a great suggestion. Another option is to create another foal from that pair (and if you already created the embryos, this may be what you want to do), which will always be NxNr, then breed those foals together. There’s a 1 in 4 chance the third gen foal will be NrNr. As Fallen stated, if you used a hom Axiom red (if Mystery Rum was a colt, that would be a good choice), your odds of an NrNr third gen foal are even higher at 1 in 2 (50%).