Esther was still lactating when she was spayed. But at three months the kitten really ought not to be suckling (though Smidgen was quite shameless about accepting favours from Esther when he arrived and found her offering milk still!!). A few days apart would sort out the lactation as without demand she will not continue producing as her hormones will take over and dry her off. If there is an underlying health issue then medication will dry her off also.
If you take the cat away, then the kitten can not access her and the problem will be resolved. But then you are stuck with the neutering costs unless by prior arrangement with the owner.