Does Danny's ability to "shine" have any connection to Jack's insanity and the events that occur in the hotel?

The shining did not cause the events at the hotel, as it does not "bring things to life." However, the events at the hotel happened because Danny had the shining. Simply put, the hotel wanted Danny dead so his spirit could be added to the hotel, which would give it more shining. The shining is a set of abilities that include interacting with spirits, perceiving events anachronistically, and telepathic communication.

Likewise, Jack's insanity was caused by the spirits trying their best to kill Danny and add him to the hotel's collection of shining. He was simply a weapon the hotel was trying to use to get Danny's spirit. Danny attempted to use the shining to protect Jack, but ultimately failed. We do know, however, that the shining is also hereditary, and that Danny's grandmother also had the shining.

It is probable that there are a lot of family members with the shining would be in this family's history, include offspring of previous "Jacks" that could have existed, but this not explicitly stated, just implied.