You may be describing a condition called tigger thumb. The tip of the thumb snaps into a bent position and appears stuck. This is usually caused by the tendon getting caught inside its own sheath or lining. It can’t glide smoothly like it should.
The fact that you can move the joint back to a normal position is a good sign. It’s possible that just making this correction while you are holding or playing with your daughter will be enough to take care of the problem.
If there’s no change after a couple of months, then a splint can be used. The splint is made of plastic and is formed to your child’s hand. It holds the thumb in a neutral position and doesn’t allow it to bend.
This is worn all day for up to three months. A night splint is used after that to keep the problem from coming back. If there’s no correction and the trigger thumb remains, then surgery may be needed.