I am new to the idea of marriage as a sacrament and am still trying to understand the implications of it. I understand there is a difference between civil marriage and a valid sacramental marriage.
Well, not exactly.
Any **valid **marriage between the baptized is a sacrament by virtue of their baptism.
What constitutes a **valid **marriage?
For non-Catholic Christians, it means exchanging valid consent such as before a civil authority or minister authorized by the state.
For Catholics and those marrying a Catholic, it also means exchanging valid consent but according to the laws established in Catholic canon law.
For the Orthodox, who have valid apostolic succession and valid holy orders, it means exchanging valid consent according to the laws of the Orthodox Churches which in their case is before an Orthodox priest.
The above presumes no known impediments such as a prior bond.
I have also learned that Protestants are considered to have a valid sacramental marriage if there are no impediments.
Correct. And the unbaptized have valid natural marriages.
But what does it mean if there are impediments, such as an unwillingness to have children?
This would be need to be proven in what the Catholic Church calls the external forum. So, for example, by the testimony of witnesses to the Tribunal.
Otherwise, our internal disposition is presumed to match the words said during the exchange of consent.
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.
Canon 1061 §3. An invalid marriage is called putative if at least one party celebrated it in good faith, until both parties become certain of its nullity.
Are they guilty of fornication since their marriage is not valid?
The marriage is termed a putative marriage when entered into in good faith by at least one party. No, they are not committing fornication.
If the couple becomes aware of a defect of consent or intent, they can correct it themselves privately. IOW, an act of the will can correct an impediment-- a new act of valid consent can be done privately unless the impediment is public and then they would have to exchange vows publicly.
See
vatican.va/archive/ENG1104/__P46.HTM
Would (civil) divorce be wrong for a couple like this?
The answer is “maybe”.
Civil divorce indicates the permanent and irreconcilable breakdown of the marriage. Certainly every attempt should be made to save the marriage including correcting whatever defect exists.
If a person is convinced of the invalidity of their marriage and has no avenue to make it valid, such a person should seek guidance from their priest.
If a person chooses the path of civil divorce they could petition the tribunal to examine their marriage for nullity, but there is certainly no guarantee that one will be forthcoming.
In such a case, they would fall under the canons related to
separation while the bond remains.
I can suggest the book Annulment The Wedding That Was by Michael Smith Foster for an organized explanation of the Church’s teaching on marriage and nullity.
On a forum such as this you are likely to get a mixed bag of answers, some of which may not be 100% accurate.