What is the ruling on a husband inserting his finger into his wife's vagina during the daytime in Ramadan while she is not fasting and not observing the fast, and he is fasting and nothing was emitted from him, then he continued to do so until the wife vomited?

A breastfeeding woman is not allowed to break her fast unless she fears for herself or her child. Merely placing the nipple of the breast in the infant's mouth without anything coming out of you does not invalidate your fast. However, it is disliked to do so during the day of fasting for fear of invalidating it.