Can I use wood glue to fixate poster paint? With my son I made a wooden shield, glued canvas over it and then he painted the canvas with his sigil. We used poster paint (children's paint) because I remembered I could not completely wash it out of clothing.

However there seems to be wiggle room between 'not coming out in the laundry' and 'being fixated to a DIY project'. The paint does come off when wet, not completely, but enough to stain seats and clothes.

Could I use regular wood glue to fixate the paint? Just applying a thin layer? 
My other option would be varnish.

The main point is that the shield will be in use, so whatever I apply cannot be brittle. It should stay in place when the shield is hit by a wooden sword (obviously).
For a quick fix use acrylic medium which is simply clear acrylic binder; acrylic paint without the pigment. It is soluble in water, easy to thin and work with and clean up after, and it dries waterproof. Available in any art store or online. You can get it in matte or glossy or in between. That should bind the poster paint no problem. 

And for the next shield you paint, start with acrylic paints. There are affordable grades equivalent to poster or tempra paint, but they start off waterproof (when dry). And you can get higher quality colors, different thickness mediums to add texture, better range of colors, etc.

Just remember to rinse out your brushes as you use them, the acrylic will dry to waterproof in the bristles too and destroy them.

Oh... and you could use wood glue maybe thinned a bit, but it would be a poor solution. Likely to dry too slowly and the colors will bleed. Also may not have as nice of a finish, may remain sticky. Finally it will likely lead to discoloration over time. Its possible it would still be water soluble too so don't use wood glue unless there is absolutely no alternative.