Is it appropriate to have assignments due during spring break for an online course?
The student is correct, spring break is, as its name suggests, a break. The fact that no students had complained previously does not say much - students can be timid and may not complain about any mild abuse by an instructor (as I discovered recently when I accidentally kept my class going 10 minutes past its end time; no one said a word...).

Also, your own rationale that “The students have the option to get ahead [...] by a couple of weeks, so if they have a trip planned, they can do the work in advance”, seems flawed to me, as it is premised oh the assumption that students have extra time in which they are sitting around doing nothing and can redirect towards “getting ahead”. You should assume that in the normal course of things students are as busy as they can get and don’t have spare studying capacity. The option to get ahead is nice, and may be used by some especially studious/efficient students or those that want to undertake a trip during time not officially sanctioned as break time and are willing to make an extra effort and sacrifice their normal free time to catch up. But this cannot be used as justification for requiring students to study during official break time.