Yes, the court would find you to be in contempt even though you are in a two-year relationship. The particular provision in question is generally known as a "morality clause." Although these particular provisions are starting to fall out of favor with the courts, they will still enforce them if they are in the divorce agreement.
I suggest that you abide by the clause or seek to have it removed, either through an agreement with your ex-spouse or by the court itself.
Nothing contained herein shall be considered or construed as creating an attorney client relationship between the party asking the question and the attorney. All legal problems are different. The answer given is only a general response based upon the facts provided and should not be considered specific advice for your case. Always contact a lawyer for advice about your particular circumstances and issues.
Yes, the Court is likely to find you in contempt if you intentionally disregard its Order. Note that even if the father "agrees" for you to have an overnight guest, it does not preclude him from subsequently filing an action for contempt and it does not preclude the Court from finding you in contempt. If you want to have overnights with your boyfriend, it would be wise not to do so during those nights that the children are in your custody.
Note that if you do choose to have your boyfriend spend the night in violation of the Court Order, the children's father might use that decision to buttress a modification action of his own. I understand that you want to have the man you love with you, but if you act on that desire, you will be acting in contravention to the morality clause of the Court's Order.
You might consider consulting with both a family law attorney and a child specialist on this issue. Skilled child specialists are able to share important insights about how to safeguard a child's psychological interest when transitioning into a new relationship with a third party. And, of course, an experienced family law attorney can advise you regarding your desire to have overnights with your boyfriend and the potential consequences of doing so.
If you've spoken with the father and he has no objection to the overnights, you might ask an attorney about doing an Amended Consent Judgment that would modify the prior Judgement by removing the morality clause (based on you and your husband's mutual consent).
Best of luck to you.
This answer is offered for informational purposes only. It is not offered as nor does it constitute legal advice. This answer does not constitute an attorney-client relationship. Do not rely on this answer in prosecuting or defending against any criminal or civil legal action. Speak to an attorney in your area about how to protect yourself and your interests.
If you want to lose your children (or risk that) keep doing what you're doing and defy the judge. It's pretty obviousl contempt and could even cost you custody. Either get married, move out or have him move out.