I am impressed by the gravity of your inquiry and your care in the matter in that you are seeking real answers to a complicated question. May Hashem help the two of you and anyone else in need of this post.
First let's address some issues your question raised in this case, and then let's address the Halachic ramifications.
The OP states that your wife is wishing to stop practicing mikveh observance, in part, because: "She feels that these laws were developed by men, long ago, and that it's a huge burden." Also she said: "...she is fed up with the total one-sidedness of the whole situation. It's called "family purity," which suggests mutual responsibility, but the truth is, the onus is completely on her,..."
1.) One-sided onus:
There is a famous Jewish Law in all matters of ritual observance which says that "Eyd Echad Ne'emaan B'Issurim" (One witness is believed regarding permitting the potentially forbidden). (see Talmud Gittin 2b and elsewhere)
The reason I can go to your house and eat food as your guest (without personally supervising the Kashrut) is because I may trust you. In fact, the entire Kashrus industry relies on the testimony of single witnesses in factories and farms as far flung as the Pennsylvania countryside to Hong Kong.
So where in the entire Torah does it say that Hashem lets us believe the testimony of one witness? What case did Almighty G-d deem fit to represent the fact that you may utterly trust your friend's word without question in matters of spiritual life and death? Was it a case of kosher meat, a temple sacrifice, or the observance of Yom Kippur? What is the paradigm used by the Holy Torah to teach that we owe each other love and loyalty to believe a person when they tell us something?
It is the fact that a man must, by Torah Law, trust his own wife concerning the laws of family purity.
Vayikra (Levit.) 15:28 "If she ceases her flow, she must count seven days for herself and afterwards she can be purified."
The words "for herself" mean that she purifies herself privately and is believed. (Talmud Ketubot 72a) This is the source in the Torah that a single witness is privately believed. (according to Tosfos Gittin 2b)
Therefore, we now see the reason the Torah made most of the family purity process dependent on the wife's private observance. This is to obviously elevate the wife in the husband's eyes as being responsible and trustworthy. Imagine if the husband were commanded to oversee the process?! His OCD behavior and oversight of the wife's every move would certainly insult her and destroy the trust of the marriage! Instead, the Torah has the husband sit back and tell her that he trusts her. Now she is honored and the marriage grows.
2) These laws were developed by men?
R’ Zeira- B'nos Yisroel (daughters of Israel) were machmir (strict) on themselves that even if they only saw tipas dam k’chardal (a drop of blood like a mustard seed) they wait 7 nekiyim (7 clean days). (see Talmud Niddah 66a)
The Halachic system of Israel is not the result of the dictatorship of a few men. It is the published agreement of our people as a whole. Here, the above law of family purity was passed by the women of Israel on themselves. Once they did so, all of us keep it as Law.
3) Mutual Responsibility?
First of all, men abstaining is certainly a shared responsibility. But, there is also a list of laws to keep in family purity called "Har'Chakos". These laws involve both the man and woman learning a set of behaviors during Niddah. It is his responsibility. He also is required to learn and follow the private family calendar, as well as be involved in bringing questions to a Rav (she can too). All this must be done in cooperation. Furthermore, while she is preparing, he should be pitching in with the kids or other chores. The OP mentioned that they did not adhere to shomer negiah. Did the OP know of the laws of Har'Chakos; that during Niddah, shomer negiah and a host of other laws apply?
This is subjective, but I would ask that anyone claiming the purification process is a burden, really sit down and think it through before making that claim. Is checking for blood a few times, counting 7 days, and grooming oneself for a bath, really called "burdensome"? For equality sake, we can have the husband trim his nails, take a soapy shower, and go to mikvah too in preperation to meet his wife that night. :)
5) Long Ago?
Why is it a problem that these laws came from long ago? If someone invented them now, would you feel that they are more authentic??!
It has long been held by modern and non-religious communities that simply because a law is ancient, it must be wrong or changeable etc. In Judaism, we adhere to that which is authentic. So, the older its source, the better. Niddah Law is written in the Torah.
6) The OP says: "I cannot honestly say that I keep as many mitzvot as I possibly can.." as well as: "...while I have to do nothing.."
A woman's body is so intricately involved in the mitzvah of family purity that most of the technical observance falls on her. However, men have similar things. A man puts on Talis and Tefillin on his arm and head every day and davens with a minyan. A woman does not do that. Is his praying and tefillin a one sided burden on the man? Judaism has trade offs with gender roles. However, when looking at the whole picture, it is all a shared responsibility to run a Jewish home.
PENALTY FOR HAVING RELATIONS WHILE SHE IS NIDDAH?
The penalty is Kar-eys (cutting off of the soul). The source is Vayikra (Levit.) 20:18. It says that both the man and woman who willfully engage in intercourse while she is a Niddah will be "cut off".
Rav Saadia Gaon, Rashi, Tosefos, and others all hold that a basic aspect of Kareys is to die young (before your time). The Riva says before 50 - 60 years of age. In addition, there is a possibility of punishment in the afterlife as well.
For an idea of how bad Kareys really is, we can look at the Talmud and see that in Tractate Kerisos 2a, there are 36 crimes in the Torah that are punishable by Kareys.
Here are a few: Idolatry, adultery, various forms of incest, passing one's children as a sacrifice to Molech the fire god, Sabbath breaking, violating Yom Kippur, etc. Niddah is one of them.
It should make someone take pause to consider that Niddah is in the same category as the above listed crimes.Violating Niddah Laws has the same weight as violating the other 35 listed. Wow. We need to Halachically avoid this at all cost.
Finally, it seems that in any marriage, one spouse should never tell the other spouse that they are not worth as much as an equal in the marriage. If one spouse makes more money than the other, should that spouse have a separate bank account for the extra $ to hoard it away from their partner? If I happen to cook and my spouse can't or vice versa, should the cook threaten to stop cooking because the other spouse just "eats" and "consumes"? If you have been doing this for 20 years correctly, why change it?
Based on the OP, it seems you should go to an expert on Jewish law and mystical concepts who will help you understand the meaning behind the Niddah status. Once you know what it is, then you are able to live by it with proper enthusiasm.