In strict Jain conduct, a 12-year-old bathing with his mother is not automatically a sin, because intent matters a lot in Jainism.

But the strictest Jain guidance would be:

• Avoid unnecessary physical closeness and shared bathing once a child is old enough to understand modesty.
• Bathing should be done with cleanliness, simplicity, and proper decorum.
• If it is only for care, help, or safety, it is not a sinful act by itself.
• If it is done without need, the strict path would say it is better not to do it.

So the strict answer is:

It is not a sin by itself, but a strict Jain would avoid it if it is not necessary.

In Jainism, intention, necessity, and restraint are very important.