It's "funny" how in every course (often even in the courses of languages spoken in countries generally considered "progressive" like Danish or Norwegian) the children are always a women's thing. It is always "her children", "my sister's child", "she goes with her daughter", "I don't know her children", and so on and so forth. You can only very seldom find thinks like "his children...", "Peter's son...", "his son does not like...". Now downvote me as much as you want.
дети is an odd word. It only seems to have a plural form. As a plural word, in the way I've encountered it so far, gender is irrelevant, it seems, because all the articles and possessive pronouns use one form for plurals. So far, that is.
I have not been able to find a singular version of дети, and thus can't figure out what gender it is, if it has one. I also don't know how you'd figure out the ending for other cases.
The singular of дети is ребёнок. Both ребёнок and дети are male. The singular of дети used to be дитя́, and the plural of ребёнок used to be ребя́та. As far as I can tell, you will only find those forms in poetic speech or dated texts (I'm new to Russian, please correct me if I'm wrong!)