Its not normal for a broody to pick up chicks and fling them about! A good broody is such a good Mum that you have no concerns about anything, she just gets on with everything and its a joy to watch. It is quite possible that your girl is just inexperienced, and the instinct about good mothering is not strong in her, and she doesn't know what to do, and that she will get more used to it, but of course there is a risk in letting her acquire that knowledge. You have taken a decision, I don't think there is a right or wrong approach, so I would go with what you have done. Raising chicks by hand is a bit time consuming and messy, but I prefer it, because I can see exactly what is going on with each chick and can intervene quickly, but many people prefer a more natural approach and there is something special about the bonding between hen and chicks. If you feel strongly about this, then you could try putting them back perhaps later today or tomorrow and continuing to observe her. I have put 4 or 5 day old chicks under a broody successfully, but that is about the limit I would say, and of course your hen hasn't shown herself to be a good Mum so far.
Make sure the hen is OK, I am not sure how she will react to the chicks going.