I agree with AnnieBrook, RockRose, and SpecialMom. I would suggest that He may be lying and hiding His texts with His Daughter because You are expressing such dismay - He might think it's easier to lie to You than to argue with You. I too, think it's a wonderful thing for Him to be re-united with His Daughter and it would be just as wonderful if She were to be welcomed by His Wife and 2 Sons.
Truthfully, while I understand how this is aggravating, this is a HUGE deal. A father and daughter reunited? Oh my gosh. That's a wonderful thing to be encouraged. How do you catch up quickly on so many lost years of knowing one another? I would be VERY patient and if it is a deal breaker for you to have his adult daughter a very significant and frequent part of his life, I find that problematic. Now, I don't know the particulars of why they lost touch at 6 years old . . . you say a custody issue. But as a parent, I'd figure out a way to see my child . . . which he did not. Maybe the mon is tough and made it very difficult. Don't know. But what I DO know is that this young woman was RIPPED off from a very significant figure in a person's life.
I personally would love your partner through this and encourage him to be a man of strong character. Putting a child he lost touch with as his priority for a while is not too much to ask or too much for someone who loves that person to give. In my opinion. good luck
My guess is, after she visits this will die down - if only because she won't be as interested. This seems like kind of what your husband does - he attaches compulsively in an inappropriate way. But few 18 year olds want to spend most of their time texting a parent, although in her case it's probably assuaging some of the pain of his abandonment of her.
This should die down if they just got into contact recently. How long is "recently?" If this has been happening for a week that is different than if it has been happening for a year.