My daughter bought a P210 because she liked mine. At the range yesterday she couldn't insert the magazines without depressing the mag release button. Suggestions?

Sounds like a similar problem the P220 have had.

For some reason I am thinking that this was an issue for the P210 or maybe it was the P220-10mm where Sig replaced the mag release.
You might contact Sig and see if hers is of the batch that had issues.
I know I ran into this when I bought new controls for a P220 I had to have them nickel plated to change the looks and the new mag release created this issue. Applying more force when inserting overcame the problem for mine.