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When we say the blessing on commandments, such as Tefillin, there is a dagesh in the דּ of קדּשנו.
From what I have learnt a dagesh lene occurs when the בגד כפת starts a syllable and is not preceded by a vowel.
In קדּשנו the ק takes a vowel and breaks this rule. Is the dagesh in this instance a forte?
You have this one basically figured out. The dagesh there is indeed a dagesh forte, and thus the /d/ sound is to be geminated.
This word is in the Pi'el form and, generally speaking, Pi'el verbs take a dagesh forte in the middle consonant when possible.
