We appreciate the sensitive nature of this question.
We’re sorry to hear that the first childbirth was so difficult for your wife, and value how important it is to you to be able to support her.
While you are correct that the harchakot are connected with concerns about intimacy, once in place they cannot be fully waived. Harchakot are actually not freely set aside when the wife is sick. For example, there is substantial halachic debate about the permissibility of a man taking his wife’s pulse when she is in niddah, even if she is sick and he a physician. Bathing her is generally not permitted. (Read more here.)
The harchakah of not touching, in particular, is treated with great stringency, because it is arguably in violation of an independent Torah-level prohibition, when the touching is affectionate.
What can be done, then, to ease your wife’s distress and to enable you to support her?
Most important is to know that the harchakot typically do not kick in at the beginning of labor. We follow the halachic position that a woman only becomes niddah when she has bleeding or staining of the sort that would make a woman niddah (for more details, please see our pages on niddah, stains, and toilet paper), or she cannot walk without assistance (because of contractions, not because of an external cause like an epidural), or she is fully dilated. (Read more here.) At earlier stages, no harchakot apply. There is also no obligation to check for bleeding or dilation except as medically warranted, nor must you ask the physician or attending midwife or nurse if blood was observed.
Some of the harchakot are, in fact, waived even once the couple are prohibited to each other, because childbirth is life-threatening. Most relevant here is that you can freely pass things to your wife, including food or drink, during labor.
Sometimes touch really can make a difference, though. You and your wife might consider arranging for her mother, a close family member or friend, or a doula to be present at the childbirth, to provide her with comforting and even therapeutic touch.
In some cases of extreme emotional distress during labor, where the wife specifically wants to be comforted by her husband’s touch, there is room for the husband to touch his wife with a gloved hand. The same is true for cases of great physical need, where no staff is on hand to assist her.
We hope that this response has been helpful to you. Please do not hesitate to write back with any follow up questions.