So would I be right in saying the literal translation of the second phrase would be: "I want to give (送) flowers to (给) her" ？ ...我想给她送花 was also accepted.
送 means "to send without any payment", whereas 给 means "to give".
So your answer also matches the meaning and context of the sentence.
They are both interchangeable, although the given translation is more colloquial, at least in the region I learnt the language.
Actually , there's a special construstion "送+给+谁"。So,it can be used only like , not the wat it is presented in the example