Read more tag acting weirdly

Hello there,
the “Read More” tag is acting weirdly.
Sometimes the tag doesn’t appear where I want it to be, some other times it appears when we didn’t insert it.
In the post with the title “Christmas in l’Arrabassada — Pre-primary”, there’s a “Read More” tag before the second picture.
In the post “1ST & 2ND GRADERS, FIRST TERM” there is no “Read More” tag, but the blog shows no content. Instead it shows a “Read More” button.
What are we doing wrong?
Thank you in advance,
Edward A. Lockhart