Can a Catholic have communion if they married outside of the Catholic Church? My husband and I were married by a Protestant pastor, not a Catholic Priest. I have returned to the Catholic Church a couple of decades later. Can I participate in communion, or does my husband have to agree to marry me a second time in the Catholic Church?

If it matters, my husband was raised in a non-denominational Christian Church, and I was raised Catholic, but attended non-denominational Church after college.
About receiving communion currently

Based on this guidance from the Catechism, unless you've been adhering to the annual "Easter Duty" you may need to go to confession first before you receive communion. (It may be that simple). 


  CC 1389 The Church obliges the faithful to take part in the Divine Liturgy on Sundays and feast days and, prepared by the sacrament of Reconciliation{aka confession} to receive the Eucharist at least once a year, if possible during the Easter season.  But the Church strongly encourages the faithful to receive the holy Eucharist on Sundays and feast days, or more often still, even daily.  


About your marriage

You may be seeking to convalidate your marriage.  Based on what you've presented in your question, there aren't enough details to assess whether or not the Church would find it to be sacramental. (Canon Law;  1060 Marriage possesses the favor of law; therefore, in a case of doubt, the validity of a marriage must be upheld until the contrary is proven).    

How to convalidate the marriage


Meet with your local Catholic pastor, explain the situation you find yourselves in, and the details of your marriage, and he will be able to advise you on the path to take for your particular situation. Details matter.  


  In Catholic canon law, a validation of marriage or convalidation of marriage is the validation of a Catholic putative marriage.  A putative marriage is one when at least one party to the marriage wrongly believes it to be valid. 

Convalidation is not "getting married a second time" but it is a method by which the Church officially confirms that the marriage is indeed sacramental.  (In my experience, there was usually a rite or ceremony or celebration of varying complexity depending on the wishes of the couple).  The difference between a licit and a valid marriage may seem obscure, but from the point of view of adhering to Canon Law it matters to the Church. (The Church, to affirm any marriage, has to follow its own rules).       

Based on the Catholic Canon Law a valid marriage requires certain elements:   


  THE FORM OF THE CELEBRATION OF MARRIAGE
  Can.  1108 §1. Only those marriages are valid which are contracted
  before the local ordinary, pastor, or a priest or deacon delegated by
  either of them, who assist, and before two witnesses according to the
  rules expressed in the following canons and without prejudice to the
  exceptions mentioned in cann. ⇒ 144, ⇒ 1112, §1, ⇒ 1116, and ⇒ 1127,
  §§1-2.
  Can.  1117 The form established above must be observed if at least one of the parties contracting marriage was baptized in the Catholic Church or received into it and has not defected from it by a formal act, without prejudice to the prescripts of ⇒ can. 1127, §2.  


The most likely finding by the pastor, since you are the Catholic party, would be technically termed "a defect of form" since you joined in matrimony under other circumstances than are called for by Canon Law.  That doesn't mean that your bond is not sacramental, particularly as you are both baptized, but the Church has to look into all particulars to confirm that.   
You may not be able to receive communion until convalidation, but you may, since the details of your situation matter(see the above about guidance on communion).  Your situation needs to be laid out to the pastor and discussed in detail so that you can get the advice that suits your situation.  

If you'd like to take it a step higher, go to your local diocese at the Chancery.  They can advise you on how your marriage can be convalidated in your diocese.  There may be other reasons for the Church to find the marriage invalid1  


If your case is one where your consent upholds as it did on the day you took your vows, but the "defect of form" is found(as above), and you are still married, you may be eligible for a radical sanation


  Can.  1161 §1. The radical sanation of an invalid marriage is its convalidation without the renewal of consent, which is granted by competent authority and entails the dispensation from an impediment, if there is one, and from canonical form, if it was not observed, and the retroactivity of canonical effects. {My deacon used to call this "short form" convalidation} 
  
  §2. Convalidation occurs at the moment of the granting of the favor.
  Retroactivity, however, is understood to extend to the moment of the
  celebration of the marriage unless other provision is expressly made.
  
  §3. A radical sanation is not to be granted unless it is probable that
  the parties wish to persevere in conjugal life.  
  
  Can.  1163 §1. A marriage which is invalid because of an impediment or a defect of legitimate form can be sanated provided that the consent of each party perseveres.  




We have a number of questions and answers on convalidation, to include these two here.
3  and 2.  

If you search for the tags marriage, Catholicism and convalidate (or convalidation) you'll find a number of other questions (with answers) similar to yours. 



One of the things I learned in the RCIA ministry is that in the case of marriage between two baptized persons, if one of them is Catholic then the Catholic Church expects the Catholic party to adhere to Canon Law, but it does not require that the other party become Catholic for marriage.  Since you have already married outside of the Catholic Church, it can get a bit more complicated, but it may be very simple (and accepted as sacramental) if neither of you was ever married previously.  So once again, sit down with a priest and discuss the details.  


  Can.  1059 Even if only one party is Catholic, the marriage of Catholics is governed not only by divine law but also by canon law, without prejudice to the competence of civil authority concerning the merely civil effects of the same marriage.   
  
  Can.  1060 Marriage possesses the favor of law; therefore, in a case of doubt, the validity of a marriage must be upheld until the contrary is proven.
  
  Can.  1107 Even if a marriage was entered into invalidly by reason of an impediment or a defect of form, the consent given is presumed to persist until its revocation is established.  




1 MIXED MARRIAGES  


  Can.  1124 Without express permission of the competent authority, a
  marriage is prohibited between two baptized persons of whom one is
  baptized in the Catholic Church or received into it after baptism and
  has not defected from it by a formal act and the other of whom is
  enrolled in a Church or ecclesial community not in full communion with
  the Catholic Church.
  
  Can.  1125 The local ordinary can grant a permission of this kind if
  there is a just and reasonable cause. He is not to grant it unless the
  following conditions have been fulfilled:
  
  1/ the Catholic party is to declare that he or she is prepared to
  remove dangers of defecting from the faith and is to make a sincere
  promise to do all in his or her power so that all offspring are
  baptized and brought up in the Catholic Church;
  
  2/ the other party is to be informed at an appropriate time about the
  promises which the Catholic party is to make, in such a way that it is
  certain that he or she is truly aware of the promise and obligation of
  the Catholic party;
  
  3/ both parties are to be instructed about the purposes and essential
  properties of marriage which neither of the contracting parties is to
  exclude.