You file the response with the court and you send the response to your wife's attorney. If you are not hiring an attorney right away, your court probably has a self-help center. It's a good idea to have the staff at the self-help center review your paperwork to make sure you have completed it properly and that you have not compromised your position unnecessarily.
Her lawyer. She does not need to be served with any court filings.
The response given is not intended to create, nor does it create an ongoing duty to respond to questions. The response does not form an attorney-client relationship, nor is it intended to be anything other than the educated opinion of the author. It should not be relied upon as legal advice. The response given is based upon the limited facts provided by the person asking the question. To the extent additional or different facts exist, the response might possibly change.
As long as she's represented by counsel, you serve her lawyer. I agree with my colleague tjhat you should seek some professional legal advice, since you've got a lawyer on the other side.
Besides the free family lawyers available in your local courthouse (linked belkow), you should also read a book or two on the dissolution process, like the one linked below. Better yet, hire your own lawyer.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
You can technically serve either your wife or her lawyer, but it is definitely better for you to serve her lawyer. Since you're filing a response, you need only serve her by mail, not in-person. Two reminders: 1) As a party to the action, you cannot be the one to serve any documents. Someone else over the age of 18 must fill out the Proof of Service. 2) Be sure to file the Response AND the Proof of Service with the Court. You can serve her an unfiled copy of the Response in order to file both the Response and Proof of Service at the same time.