Go ahead and renew your national passport. Realistically speaking, you will have extreme difficulty obtaining visas to European countries on a refugee document.
Behar Intl. Counsel 619.234.5962 Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.
I would use RTD only. While a number of my clients have used their own passports without any problems the authorities may frown upon your using your passport because by doing so you place yourself under protection of the country you sought asylum from.
Right now you have a 'split decision' from my colleagues.
Normally I fully support Mr. Behar's opinions. But, in this case, even though he's correct in stating that a RTD makes it difficult to get a Schengen Visa ... I would be concerned about you renewing a passport of the country you claimed you feared.
I would suggest the RTD .. and a Schengen application as the safest course of action.
Plus, it is always wise to have an attorney help you.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- firstname.lastname@example.org -- www.capriotti.com -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.