Our keeper rolls it out and then disappears from the attack

The best way to get them to trust the keeper is to make them realize the keeper is actually an attacking weapon. Try playing a 5v5 game where a goal scored after a pass from the keeper counts as two. It forces the outfielders to look for the keeper as a way to recycle play or switch the angle, rather than just seeing them as someone to hide behind when they are stuck. Keep the pitch wide so there is space for the keeper to step up and offer an angle. Focus your coaching on encouraging the nearest player to check their shoulder to see if the keeper is available. If you see the keeper hanging back while the team attacks, leave it alone for a bit. Let them figure out that staying involved gives them a better view of the game and another chance to influence the result.