If we start from the context of 'rebel group', we're going to miss all of the nuances of this issue. The fact is, a 'rebel group' only comes into existence when there is a long-term and pervasive dissatisfaction in a greater population. The IRA, Hezbollah, FARC, the KKK, and other violent militancies all arose because some group felt that 'their people' and 'their way of life' were being attacked, suppressed, oppressed, or otherwise harmed by some 'outsider': respectively, the British, Israel, the corrupt Columbian government, and Federal (Northern) aggressors. That pervasive dissatisfaction encourages the angrier members of the group to stand up and make themselves heard.
- Some of those people bring their anger to an intellectual, diplomatic approach, and try to create political, legal, or social changes that will relieve the perceives oppression.
- Some of those people dismiss the idea that the other side will be 'reasonable', and bring their anger to violent attacks or organized resistance.
The latter are what we commonly refer to as 'rebel groups', but it's important to see that they are an organic result of the larger group's perceived oppression. It's not as though a group of people woke up one morning and thought: "Hey, you know what I'd like to do today? Blow up a market!" There has to be a full head of angry steam in the population before a rebel group gets off the ground.
As to why some more rational political parties retain their militant wings... Well, first, a political party is by definition part of the first group — who bring their anger to an intellectual, diplomatic approach — and people from the second group often dismiss the first group as weak and ineffectual. Rebel groups might maintain ties with political parties out of common interests, but people only get to the point of being a rebel because they are convinced 'normal' political solutions don't have a chance in hell of succeeding. They don't take orders from the party; at best, they might decide to cooperate with it.
On the other hand, even the most reasonable political party knows that radicalized elements have their usefulness. Sometimes the threat of irrational political violence is the only thing that will bring a recalcitrant political opposition to the table. I'm certain it's a common tactic for a political party to say: "We cannot control those rebels, but if you were to implement these kinds of political changes it would calm them down and keep them from committing political violence". Most political parties work on the assumptions that meaningful reforms will translate to a lessening of the sense of oppression in the population, and thus less support for more extreme expressions of that dissatisfaction. But only the most high-minded politicians are above leveraging the existence of political violence to reach their goal.
Note that this is generalizable: actual violence isn't necessary, and the same dynamic works on many levels. For instance, passive resistance movements — Ghandi's Indian Nationalist movement, Martin Luther King's Civil Right's approach, and the current protests against police brutality — achieve their ends by forcing the oppressor to recognize and be disturbed by said oppressor's own tendencies towards violence. These movements succeed when the oppressor becomes disgusted and shamed by his own bestiality. Likewise secessionists use the threat of defensive violence to achieve their ends, in the sense of: "We will not do what you say, and if you come after us there will be trouble." The implication of potential violence is a feature of many different political arenas, because the implication of violence carries with it a number of moral concerns that work powerfully on the human psyche.