I'm going to copy/paste from an earlier answer of mine, which covers most ofw hat I want to say:

Parliamentary divorce was a costly process only available to the wealthy, which required the details of the case to be presented to and dissected by members of the government; it would at least result in both ex-spouses being able to marry again, where a legal separation through the religious Doctor's Commons did not allow remarriage. It was almost always initiated by the husband: women needed to prove a pattern of extreme abuse on their husband's part as well as flagrant infidelity or desertion, while a man who could prove without a doubt that his wife had been unfaithful to him sexually would be much more likely to have his responsibility for her ended. (The southern American colonies followed this standard, while in the non-Anglican north divorce was seen as preferable to the social disruption of marital violence or sinful adultery, and so somewhat more accepted and easier to get for both women and men.)

Note of clarification: for the proof of adultery, typically a husband pursuing a divorce would sue the man he accused of being his wife's lover for "criminal conversation", a euphemism for adulterous sex. If he won, he could then progress to a divorce with the proof in hand, or he could simply leave his wife's reputation in tatters but with no possibility for remarriage to repair it - in either case, he was typically rewarded with damages from the other man involved.

Following a divorce, the former wife was in a bad situation. She had none of the property she'd brought to the marriage, and was no longer being supported by her husband, so she had to hope that either her birth family or the man she had been involved with would take her on. She had also been publicly branded as disreputable - a whore, essentially - and would be shunned, which would give both her family and her lover pause, since associating with her could tarnish their own reputations. At least in the case of a parliamentary divorce, she had the hope of remarrying, which could mend her problems somewhat; if the case had gone through the ecclesiastical court, she was simply ruined forever.

At this time, children were viewed in the legal system as the property of their father, and it was also considered in their best interest to remain in paternal custody (except in cases where the fathers were exceptionally abusive and neglectful, at least in America). Even in a normal marriage, mothers weren't automatically considered their children's guardians after the father's death unless it was stipulated in his will, and fathers could apprentice their children wherever they wanted without the mother's consent. Due to both the the lack of amicability in divorces and the social stigma placed on the heads of women who engaged in extramarital affairs against their husbands' wishes, the fathers were typically unlikely to allow ex-wives any contact with their children.

In the late eighteenth century, two things were happening that affected this. One is that divorces were becoming more common than ever. Though they were still difficult and embarrassing to get and still carried a social stigma, the number of divorce cases rose and rose. (As did court cases charging "criminal conversation" - husbands filing suit against men they believed to be sleeping with their wives.) In Massachusetts, for instance, only six divorce petitions were filed between 1705 and 1714, but there were 46 between 1765 and 1774, and almost 90 between 1775 and 1784! In Britain, there were a number of high-profile divorces between aristocratic spouses that would have also helped to raise awareness of the possibility.

Divorced women were not inherently entitled to either alimony or visitation rights - they would have to sue for them themselves, or have their lawyers work with their ex-husbands' lawyers to draw up a settlement on the subject. And this did happen! However, these payments were typically low, and ex-husbands often avoided paying them. Divorced wives generally returned to their birth families, in any case: not only was it usually required by the state of their finances, but it was a kind of reversion to the pre-married state, where it would not be considered appropriate for a woman to live alone.

It's important to note here that Caroline Norton was able to charge her debts to her husband because she was not divorced: she was very cleverly doing some "malicious compliance" with the rules of coverture that governed married women, paralleling the unjust appropriation of her earnings as a writer by her husband. If she had been divorced or even legally separated, she would not have been able to do it.