Should a Buddhist advocate the learning of a martial art? I'm listening to a lecture series about child development and in the first lecture it advocates teaching children martial arts as an aid to enhancing their self-control. I would quite like my daughter to learn a martial art (if she wants to). However I feel a bit conflicted about it as surely the lessons themselves are learning how to assault people or at the very least engage in potentially violent behaviour.

Is it justifiable for a Buddhist to learn or advocate the learning of a martial art? I appreciate that there is a cultural connection between martial arts and Buddhism in some cultures? How are the ethics of it dealt with? Generally how can I take my daughter off to a Buddhist family retreat one week then whisk her off to learn how to attack people the next? That seems inherently conflicted? Is it?
Wholesome intent is important

The Buddha learned archery as a kshatriya, but he didn't lose his compassion - see this story of when his cousin shot down a bird.
Martial arts can connect one deeply with the body, but so can Yoga and Tai Chi.

Buddhism and violence have a long history, not always nice

Meditation was used to numb kamikaze pilots to commit suicide in WW2 Japan (source)
Buddhist kingdoms Burma and Thailand were often at war, with monks on either side sometimes disrobing to fight and even lead armies. (source) 
Shaolin monks trained in martial arts to fight off bandits, but continued to train in those skills long after the threat of bandits was gone. This has destroyed their religion and holiness. (source)

Wholesome and wise company is important.

Not everyone is going to be perfectly enlightened about martial arts, and violent people or those on a power trip are generally attracted to violence. Choosing the right teacher and school is important.
Much less risk of this with Yoga, or with nature sports like mountaineering where solitude prompts the same body awakening.

Right recognition of your level of awakening is important

Jesus walked on water, and the Buddha breathed fire and water from his nostrils, but most of us can't do that. 
Just because the Buddha remained untainted by training in martial arts is no guarantee that we will also remain so. 
And, just because as a Bodhisattva he was ready to give up his life than raise a finger doesn't mean we can all be so. 
We must rightly recognize our failings and abilities. Buddhism is not foolishness. Guilt tripping about our inability to be very non-violent is foolishness.

Creating fortunate circumstances for practicing the holy life is important

There's violence all around us, not just on the mat. Competitive sports where opponents yell at each other, or careers where colleagues fear each other are also violence. 
Just as the Buddha didn't want his monks to eat more than was enough to hold the body together, or wear more clothes than was needed to cover the body, violence in all spheres of life must be restricted to the bare minimum. 
For example, pursuing a selfishly competitive and stressful career in pursuit of vanity is violence and greed. 
If there is no vegetarian food, then animals maybe killed, but only to the bare minimum. Gluttony of even the vegetarian sort is violence and greed.
Learning violent skills when one doesn't live in violent times is needless.

Buddhism and life are not different - when there is violence in human life, how can there not be some violence in the life of a Buddhist? 
Not recommended, but Dharma can be realized even through extreme violence

King Ashoka had to feel and see the blood and gore of the Kalinga war first hand to change his views on violence - he was already a Buddhist or exposed to Buddhist views on violence, but the non-violent message didn't penetrate his being until he got a maximum dose of violence. (source)