"Glad" has no comparative.
"Gladdest" is the superlative form of "glad", not the comparative form. I believe "glad" has both forms, even if they're quite rare.
The reason "gladdest" is incorrect, is probably because you cannot place it before a noun. See first definition of the link above. According to Longman, you cannot place it before a noun. That would be my guess.
The OALD adds a note before these two expressions: (old-fashioned) bringing joy; full of joy: glad news/tidingsBut - glad news/tidings. (OALD)