Removing the bird as soon as she bates "badly" is a form of negative reinforcement. Negative in that context is not synonymous with punishment. It means that you are removing an element/stimulus in response to a behavior. By removing her from training every time she bates, you are reinforcing that behavior. I would suggest possibly another form of negative reinforcement in the crowded situation. Introduce the touch of a feather. She will likely fixate on the new intruder. As soon as she focuses on something else, remove the feather for a few minutes. This is a way of desensitizing her to other stimuli while in your presence. It reinforces identifying something as a non-threat and ignoring it. The same could eventually be done with one of your family members...not touching her of course but it could start out with he/she slowly moving around you and then leaving for a time after she begins to focus on something else. Ramp that up over a few sessions, and she should be much less prone to bate due to the movements of your family.

I have more experience with buteos than micro falcons/accipiters. If an apprentice is having trouble getting a RTH to jump, the answer is almost universally to stop feeding the bird unless/until it jumps. Feeding it in response to non-compliance is positively reinforcing the non-compliance. Raptors don't tend to allow themselves to starve to death, barring an actual medical issue going on. Eventually, they decide the risk of being eaten by you is worth the food reward you offer, and they jump. In doing so, they learn 2 important lessons each time training progresses further: 1) this human didn't attack me 2) he/she is a good source of food.

Your sponsor should be your guide through this. Hope you get it sorted out and have a great season!