First you have to get an idea of how big a place he is hold up in. Then build a duplicate. Train your men (WHo I will call the "attacking group"
on how to enter the compound and NOT kill the child. The Duplicate does NOT have to be exact, just whatever barriers the Police may face be addressed (in the training exercise, the wall can be paper, but have the Attacking Group being train to treat them as if they were solid).
You have the Attacking force that will take the compound do it over and over again, so that it becomes second nature to them. Military units do this all the time, if they know the actual operation they will be performing, they do it over and over again till it is automatic with them.
Once the attacking force is trained, you wait till the best possible time. Best when the Hostage taker is asleep. Over a few days an observer will notice when the hostage holder sleeps and where, that is given to the attacking group who modify they plans accordingly.
Then the attack order is given and the attack group goes in. Te operation is over is 2-5 seconds.
Please note the Attacking force does NOT have to be near where they are attacking while they are training. They can be at a Central Location where they can train in secret and then driven or flown to the site where they are to take out the Hostage Taker.
Such an operation has to take a few days, to rush it is to go in NOT knowing where the Hostage taker is, NOT knowing where the Hostage is AND not trained so that everything comes automatically to the attacking force.
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