not possible to answer a question about an individual marriage situation here, since each is unique. in general, when you begin the process of preparing to enter the Catholic Church, called RCIA, you will begin with an interview between you and that pastor, or his delegate, to deal with exactly such questions, and otherwise ascertain your needs in regard to the process. Be prepared to give as complete and accurate info as you can about your current marriage, and former marriages of either spouse, and about the exes–were they baptized, were they Catholic etc.
from that he will determine what must be done next. In general, the Catholic Church recognizes as valid marriages between non-Catholics, assuming they were otherwise free to marry. Someone who has been previously married and divorced was not free to marry, unless that first marriage was invalid from its inception. A formal investigation by the canon law tribunal is the means by which the validity of that prior marriage is judged.
If the first marriage was between a Catholic and a non-Catholic, however, it may be invalid because of a number of reasons having to do with laws that bind only Catholics, and may not need a full investigation, but still needs to be addressed.
as many parties are involved in the current and prior marriages, is as many pieces of the puzzle that need to be looked at. bottom line, it is usually a lot easier than this sounds, esp. if one of the “old” marriages involved a Catholic who was not married in the church. that is why gathering all the relevant info is so important.
dont be deterred by the sound of this from speaking to the priest at your closest parish ASAP, because some parishes have classes forming now, and in any case, the sooner you find out where you stand, the closer you are to getting an answer that applies to you.