I understand that this is irritating to you. I usually prefer to have my items unmarked.
But -
Is this a bit of a control issue between the two of you?
Are these items really all that important? Are these $500 books or relatively inexpensive books?
Is your second child even born yet?
Even at a young age, I think children need to learn the concepts of mine, yours, and ours. And when it's appropriate or NOT appropriate to share, lend, or borrow