Separate tickers means you are not connecting.
DL won't rebook you if it is late and IB won't either (unless you have a fully flexible fare) if you miss it's flight.
Without a proper connection DL you are also looking at DL not interlining your bags to IB and so that means collecting them and the time it takes to do that
You say you have 3 hours. Have you allowed for the IB bag drop cut off time?