The practice of splitting the kingdom between sons (e.g. Charlemagne's heirs) was intended to prevent conflict because of there being only one heir to the throne. And, in other areas where primigeniture wasn't the rule (Holy Roman Empire, Poland, Ottomans, etc) it just wouldn't happen.

In addition, you did have cases where the ruling king (or queen) set their preferred candidate as heir, which was then ignored after death (the events leading to the Anarchy in England being a good example).

In extreme cases, the ruling king could have disqualified a disfavored heir by forcing them to join a monastery, disinheriting them for some reason, or possibly trumping up a charge against them, but I can't think of an example offhand better than Justinian having Belisarius blinded, which is only barely applicable.