Is this sentence correct?

kore ha himitsu desu. Dare mo ni iwanaide kudasai.
[This is a secret. Please do not tell (to) anyone]
I ask this because eventually there is a need of object marker, since in the second sentence still refers to the "himitsu" in the first one.
Also I have a problem with the syntax part of "dare mo".. Is it "dare mo ni" or "dare ni mo"? According to sources tge latter is applied, but is the other one necessarily incorrect, I wonder

I think it's correct except the dare mo ni part. As you said, it should be dare ni mo.
As to whether or not the other way is grammatically forbidden I can't say. I've never heard that phrasing.