You should be allowed to watch - it's your horse.
A good trainer will want you to watch so that you will know what to do with them afterwards. When I help people I will only do it in their presence.
A good trainer will not hurt your horse and will make everything very clear to you and your horse and works calmly and slowly.
The horse should seem happier at the end of each session - not stressed or upset or nervous. Good trainers always have that as their goal - no matter what has happened during the session.
Have I said too much or does that help?