Can my boyfriend’s wife keep me away from their daughter?

The Wife can try but I do not know what the outcome will be.

Yes if she can show it is in the best interest of the child or if she has grounds to obtain a restraining order to keep you away from herself and the child.

There must be a reason why your time with the daughter is bad for the daughter.

Depends upon what you have done. Have you threatened to harm the wife or the child?

Not an easy question. Most ex-partners are jealous of the new partner - and especially when the new partner is interacting with the child as is happening here it seems. It some cases I have seen a court order no interaction with a third party (you) when the new partner has a criminal history, or other attributes that make the relationship not in the best interests of the child. It can be done much more easily where issues of harassment or domestic violence are prevalent under the terms of a Temporary or Permanent Restraining Order. For that to happen, you would have had to act in a very definite way. However, if you are responsible person with no adverse history, the court will recognize that you might eventually be the new fiance or step-mom. Here the courts will recognize your bf's right to move on.

Yes, she can file an injunction to keep you away. The decision, of course, will be up to the Court.

No, but the court could restrict his visitation if it was convinced that you posed a danger to the child. Normally, that occurs only if the non-parent is a convicted felon or child molester.

She can try. But, unless she can prove some "unfit" quality drugs, alcohol, abuse, etc., she probably will not be able to keep you away from the child. Be prepared for a lot of accusations. Also be prepared for the argument that "it is too soon for the child to understand" that the parties are getting divorced, for another woman to be in the place of the wife, etc.