I just wanted you to explain me the following rule.
1) She promised to drive me to the station.
She promised she would drive me to the station.
Can "promise" ever be followed by "to + indirect object or indirect object"?
Ex. She promised her mum (OR to her mum?) that she wouldn't tell any more lies.
Yes, you can have either an indirect object (she promised her mum...) or a prepositional phrase (she promised to her mum...) after "promised." If you have an indirect object, there is a different phrasing afterwards than if you have a prepositional phrase.
Examples:
She promised me that she'd drive me to the station.
She promised to drive me to the station. (neither IO nor prepositional phrase here)
She promised to me that she wouldn't drive anyone else to the station.
Let me know if this doesn't make sense.