A disobedient child who did not care for their parents — do they still inherit?

Yes. Disobedience to parents is a major sin, but it does not cancel the right to inherit; the only bars to inheritance are difference of religion, killing the deceased and slavery.
Allah sets each child's share in an-Nisa' 4:11 without tying it to conduct. The Prophet ﷺ said that a Muslim does not inherit from a disbeliever, nor the reverse (Sahih al-Bukhari 6764), and scholars add that a killer does not inherit from the one he killed. Parents cannot deny a child's share by bequest, since a bequest to an heir or beyond one third needs the heirs' consent. A lifetime gift to the child who cared for the parents is allowed if it is not intended to wrong the other children and is made fairly. Disobedience will still be answered for before Allah (al-Isra' 17:23). See Faraid.