So here's I thought on the peanut thing but as a different view.
2 of my 3 sons were lactose intolerant when they were infants, I breastfeed. Normally this isn't so much an issue breastfeeding as it can be with formula. But it did result in both times i had to cut all dairy from my diet so none would pass on to my children via nursing. It can take any where from 2-4 weeks for dairy to leave a moms body.
So back to the chickens, yes it's possible to pass on the enzymes that produce an allergic reaction. Give it a month at least of peanut free feed, offer her a dozen for free to try. But honestly the part I can't say for sure is possible cross contamination, poop in the run for example could have peanut enzymes picked up on thier feet or feathers and passed back to the shells of the eggs, I don't know if this would be enough to cuase him to react further... So don't be surprised if she won't but eggs from you any more.
Your best bet to remove all trace of peanut would be to set up a second coop away from the first and after the peanut free feed time remove a select number of hens to the new coop for strictly peanut free production. As this would be the best method to eliminate any cross contamination
*add* if you are willing to do a peanut free coop, it might be wise to wash the hens to move really well with dawn. Dry them and as its likely cold there right now give then a warming light for a few hours untill all are fully dry again.
