A couple has been married for 20 years. He came from an observant background; she didn't, but she consented to go to the mikvah each month to uphold the laws of "family purity". Over time she has become more resentful that the whole burden is placed on the woman. The man came to Mi Yodeya to ask what halachic leniencies or remedies might be available.
Others covered the halacha better than I did, but I spent most of my answer on the question behind the question:
Halachically, you transgress a biblical commandment if you knowingly have relations with a niddah, and the punishment is karet. Another answer cites Rambam Laws of Prohibitions on Relations 4:3. According to Rambam Issurei Biah 1:1 (h/t DoubleAA), punishments for forbidden relations apply to both except in a special case not applicable here.
By the way, the talmud on Ketubot 72 includes this case in a list of reasons for which a man may divorce his wife and not pay her ketubah. I know you don't want to get divorced; I'm just pointing it out as a possible consequence for other couples. (I don't know what later sources have to say about that, and one shouldn't go only on one daf of talmud.)
Having said that, I'm going to respond to the rest of what you wrote. By your report, your wife resents the niddah laws because they place the burden entirely on her -- what does she get out of this, beyond that it makes you happy? While spouses should always try to do things that bring each other happiness where possible, she's feeling burdened. It's not fair. I totally get that.
You care about her doing this and you both care about having a happy marriage. So what can you do to make this feel less one-sided? Halacha might not demand anything of you, but in the interests of infusing some positive feelings into this aspect of the marriage for both of you, I suggest you think about ways to make mikvah night special for her. Not as a bribe for going to the mikvah, but as a kindness that you do for somebody you love at a time when she's feeling burdened. You'd take some of the load off if she were sick, or stressed by work/school/kids/family, or just feeling down, right? So take some of the load off from this source of aggravation too.
What that looks like depends on the two of you, but, for example, maybe it would help if you cooked her a nice dinner that night (or took her out)? That's just one idea. Do something nice for her. From her perspective she's doing something nice (not required) for you, so if she feels like she's receiving some kindness too, maybe that'll help her feel better about it.