need to repeat the subject in a coordinate clause?

I'm editing a text and so far the sentence I'm working on looks like this:

They are the ones we wanted to pay tribute to, and remind people what they protested against.

The subject of "remind" is "we" ... is this clear? And also, is the sentence correct?

I wonder if I need to repeat the subject: "and we wanted to remind people..."

No. The comma directs to the reading

• They are the ones we wanted to pay tribute to, and they remind people what they protested against.

..............

Merely dropping the comma leads to what is probably a zeugma; better grammatically would be

• They are the ones we wanted to pay tribute to and the ones we wanted to remind people what they protested against.

But this is almost certainly not the intended meaning.

..............

Dropping the comma and adjusting the grammar allows the correct (resultative) reading:

• They are the ones we wanted to pay tribute to and in so doing remind people what they protested against.