No, you can't use remind in the form [subject] remind [indirect object] [direct object].
I've been searching for a while and I've been unable to find a good resource explaining it, so I've come up with the following myself (so parts of it may well be wrong). It can be summarised by saying "that's just how remind is used in English".
The best way I can think of explaining it is that the verb remind is always followed by its direct object, which I guess makes it a monotransitive verb, which is a verb that can't take an indirect object. (DISCLAIMER: the previous sentence is the bit I'm not quite sure about, someone more knowledgeable may end up refuting this.) However, as more explanation is usually required when using "remind" (to explain what should be, is being or was remembered), it can be followed by either:
- Nothing, if the thing being remembered has already been established (e.g. "Thanks for reminding me"),
- A prepositional phrase (usually using "of", but sometimes "about"), if a "thing" (i.e. noun or noun phrase) is being remembered (e.g. "You remind me of my sister" or "Remind him about dinner at the weekend"),
- A to-infinitive, if an action is being remembered (e.g. "Remind me to reply to that email"), or
- A "that" clause, if the thing being remembered forms a clause (e.g. "She reminded me that the conference is on Tuesday"). Sometimes the "that" is left out, but is still implicit (e.g. "I reminded him (that) we are meeting tomorrow")
Therefore, out of the possible sentences you have provided, only the one that includes "of" is grammatically correct. The example with "to" in is using "to" as a preposition, so is not correct. It would be correct if it was used in a to-infinitive, e.g. "This song reminds your children to call me".