You have a piece of paper, a document, issued by the court stating that your child's father had to pay your daughter $1100 per month for child support. That, my dear, is a court order. Your child's father has been violating that court order for 11 years. $1100 X 12 months X 9 years = $118,800 that he owes in back child support. That money belongs to your daughter toward her care, her education, etc.
Custody and child support are two separate issues. It's not a situation where "If a parent pays child support then that entitles them to custody." Being her father and his wish to pursue a relationship with her would entitle him to custody or at least visitation even if he never, ever pays a penny of child support. Just so we're clear.
I think it's a really bad idea to go behind your husband's back on this. It's dishonest and secretive, and there's no reason for it. You don't need his permission to pursue the child support for your eldest daughter because it's for her benefit UNLESS your daughter's father legally gave up parental rights through the courts and your current husband adopted this daughter. That's another avenue you could take, by the way. You would have to provide appropriate notification to your eldest daughter's father to get the process moving if your husband is willing to adopt her, if she's willing to be adopted by him, if you're willing to have him adopt her, etc.
But if you keep this a secret, you risk losing a lot of trust in your marriage and doing a lot of damage. Remind him that while you guys may not "need" the money, it will be an investment in the girl's future. It's HER money. Put it in the bank. Pay for her college with it. Pay for her wedding or a down payment on a house. Put it into a revocable trust to do whatever she wants with it when she turns 25. Let it earn money in there. It will help her make a good start on her life when she's starting out and needs the money, and it will be HER money.