The position is a delicate one.
Technically she does need the agreement of the father or and Order from the Family Court to take the Child out of the Country.
If she does do so then the father can make an applictaion to the court in the UK to force her return to Texas whilst the family Court decides what is best for the child.
The Hague Convention - which covers these matters - also says that the matter should be dealt with by the Courts of the country in which the child resides - and that "residence" is decided by where the child has lived for the last six months.
At present there is an argument for saying that the residence of the child in Texas has not yet been fixed and that accordingly your daughter can bring the child here and the UK courts can decide what the long term position should be.
Clearly the longer that the child is in Texas the harder it will be to argue this.
There is an element of risk.
From what you have said it was always planned that the child would reside permanently in Texas - but there is sufficient grey are involved that she could be successful if she came her and made an immediate applictaion for a Child Arrangement Order stating that the child will live with her
Please ask if you need further details