You need to calmly assess your options and make sure you understand the issues regarding marriages [civil and sacamental], sacraments [you life and what it means to accept Christ and be baptized] and annullments [what an annullment is and what it is not] … it seems like you have misunderstood some of what you were told …
Your first mistake was marrying a catholic without having the validity of your first marriage determined …
for non-catholics, being married before a justice of the peace, civil ceremony or in religious ceremony may be sacramentally valid even if the marriage ends in divorce. The Catholic church starts from the position that they are valid. However, for a catholic person only a marriage witnessed by a priest or in another faith tradition with proper permissions are obtained are considered sacramental.
As for subjecting your marriage to a tribunal now - that is possible … however, the process involves both parties to the marriage - you and your former spouse … plus witnesses on both sides …
You do no need to hire a private detective … you do have to provide contact information to the diocese so that your former spouse can be contacted …
If you do not have her current address you can take reasonable steps to provide that information … hiring a private detective is one way … other methods are to provide legal notification or requests for information in geographic areas [last known address, family home town for example] contacting a friend or acquantance from when you were married, her last employer, her father’s church, her high school or college …
I had a friend who had to go through this exercise … they even went to the local library to access telephone directories for several locations [his last nown residence, his mother’s last know residence]. They even called the numbers of people with the same last name. My friend did not have a lot of money and she was marrying a gentleman who was disabled … they spent months documenting their efforts to locate her ex-husband … doing the leg work [which was harder then - no internet and PC’s - long distance phone call charges, etc] …They also did all of this before getting married and they never co-habitated either … they were dedicaed to each other and having a sacramental marriage - union united with the Holy Spirit

they did not set a date until they knew they could truly be united as one.
The key is to make a real effort to provide contact information … document all of your attempts, every effort you make …you will probably find her … you have children together - that is a factor - you were married for 4 years - you must know where you can start a search …
You could live seperately from your spouse - living not as husband and wife - no carnal relations … as you work thorugh this marriage issue… as others have noted - it is not that you are divorced that is keeping you from the sacraments - the issue is that you have contracted a marriage when you may [or may not] have been free to do so … plus you married a catholic outside the church - definately not a recognized marrage for both of you - even if you never had been married …
Whether or not your former spouse was baptized may factor in how the tribunal interprets the evidence of understanding and intent as to the sacramentality of the first marriage but it would not matter if that baptism was as a catholic or another faith tradition … if your former spouse had been catholic and married you by a justice of the peace then th marriage would not have been recognized … so evidence of her baptism may have bearing … .
Good Luck and God Bless, I know th eturmoil of the annullment process first hand … I subjected my first marriage to this scrutiny … not easy but it is healing