Blacksmith
Since she was a blacksmith's daughter, it was proper for Gwen to learn about her father's trade. After all, her most likely future was probably to become a blacksmith's wife, and so she will have to know such things to assist her husband.
However, it was not proper for her to don a leather vest and gloves, stoke up the fires and actually smith.
But Tom did teach her, and taught her well. He saw no reason not to teach Gwen. That's how it was done- he was taught by his father, so why should he stop just because he had a daughter?
Gwen was grateful he did so- everything her father had taught her, she found valuable. She had used those skills in number of occasions. So as her father had taught her, Gwen taught to her own sons. Many were aghast at this, finding the whole thing scandalous and completely barmy. They have questioned on what the king thought of the princes spending their days in a smoke-filled dirty forge and learning how to smith.
Gwen found this amusing- it was Arthur's idea.
Learning the basics of the trade would be good for the boys. They would know how to repair armor and weapons should the need arise. It would also help them be aware of the work put into making the things they use every day. And it was their mother's heritage they were learning and be proud of.
Her sons could be proud of her and their grandfather Tom, the forger of Excalibur.
Gwen would talk about Tom during these lessons. How he did his work, the good times they had, and the kind of the father he was.
The boys craved these discussions- they were curious about their grandfather. To hear their mother to talk about her father so earnestly and readily, to be connected in that way, was enough to look forward to the sessions.
To the actual learning of the trade, well, her boys could be decent blacksmiths, perfectly qualified to do their own repair work and inspect metal work, but they all took to it differently. With her first three, the lessons stopped after a few years.
Amhar appreciated the practical sense of it; Jack had an intellectual curiosity about it; and Gwydre desired only the end result.
Duran, her youngest however, loved the process, the feel of the steel and ash, and fire, the melting and cooling of the metal and its taking shape.
When she showed him how to forge a sword, Duran had a studious gaze, enthusiastic for the lesson that was absent in his brothers. He readily took the tools to follow her example, cautious in his movements and listen to her advice.
Once done, he showed her his first sword. She inspected it with keen eyes.
She remembered how her first sword was a bit off balanced. Duran managed to make the blade smooth, but the handle was slightly off centered.
It was good first try.