Praise be to Allah.
Yes, repentance from a particular sin is acceptable even if the repentant insists on another sin which is of a different nature and not the same as the one from which he has repented. For example, if a man repents from having accepted interest but not from drinking wine, his repentance over accepting interest is acceptable, and vice versa. But if he repents from simple interest but not compound interest then his repentance is invalid. Or if he repents from taking drugs but insists on drinking wine, or vice versa, then the repentance is invalid too. It will also be incorrect and unacceptable if a man repents from adultery with one woman but commits it with another. In all of these cases they have only shifted from one variety of sin to another within the same kind.
And Allah knows best.