To be honest, the whole process involves revisiting the past. Social workers will want to know that you have processed all of those events in your life both together and as a couple.
They will pull at any loose threads and this is a big loose thread.
They would want to know why you felt you owed your ex confidentiality over total honesty in your current relationship, especially given that it was official and has a direct impact on your relationship now. You owe him nothing at all. There is no such thing as confidentiality in this process really!
They also need to know whether you have really been able to process that time in your life. For example, would you know the signs of another abusive relationship? What tools or strategies would you have to escape it? Being a new parent absolutely kicks you in the gonads mental health wise, and you can be incredibly vulnerable, so having a robustly set of strategies to prevent your own isolation would be important. I would say it is a strengrh- you have clearly done it before, so you could talk about this as a positive aspect.
I would also say that having a kid can be very triggering, and adopted kids can be incredibly astute about working out your triggers. For example, if you like a tidy house because your mum/ex/uni flatmate was messy, or insisted on it or mentioned it once when you were feeling vulnerable, the sound of a million tiny lego pieces tumbling to the floor as your child gleefully empties a box with nary a care in the world about them going everywhere for the tenth time that day might well be the last straw. I would say that you need to have processed everything that happened with your ex with your new partner so that they can know why you reacted that way and can support you. It also means you can name your own feelings.
Finally, there is also a lot of life story work involved for adoptedchildren. You tell them stories, retell them, play them out, help them to make sense of it. The breach of trust between you and your ex when you found out about those images must have been really hard. Your children may have gone through similar experiences, or been victims of similar circumstances. You will possibly be reliving your own trauma everything you do this, and without the support of your intimate partner that is hard.
I would say you have a really good opportunity to discuss this with your partner, and get some good learning from it that will be seen as really beneficial in your application.