I am wondering the best way to go about putting the below service together:

Andy calls a number

Andy's call is bridged to Brad

Andy and Brad have conversation

Brad then puts Andy on hold via DTMF

Putting Andy on hold triggers a call to Carol

When Carol answers she will be bridged with Brad whilst Andy is on hold

Brad will then take Andy off hold via DTMF and all 3 will be connected

Brad then hangsup and Andy and Carol are left talking until either hangsup