...What the ever-loving god-damned fuck are you going on about? Even if Taylor wasn't moderating her use of force appropriately, which she seems to have been, Joe can trust them, or tolerate them in spite of a lack of trust, because he can trust them as far as he can throw them and even without using his shiny new space-elevator Joe can metaphorically throw them into orbit.
Furthermore Lisa, however encouraged by her Shard to feel so, is terrified of Joe having a catastrophic power-interaction with other Trump capes and Brian, I'm fairly sure, is fixated on trying to maximize the ratio of perceived-risk-to-perceived-reward of anything detrimental to them for safety purposes; to put this in perspective you need to remember that Shards come with a degree of mental pollution and that Grue is a Stranger/Shaker Cape.
I was looking more at it from the perspective of Joe to be honest.
Joe's first interaction with the Undersiders was influenced by his "Agent" being happy to see them. But then he learned about what happened during the bank robbery. That terrified him and he felt responsible for giving them the knives that they ordered from him. (Although I personally find it funny that the equipment he needed to make them became obsolete within about a day or two.)
Lisa has been shown to have issues about control, which admittedly, gets worse with Joe because of how he gets new abilities and knowledge that would warrant a PRT Rating by themselves. Not to mention his personal reality that holds equipment that every Tinker would literally give their first child for to be able to spend a day in.
But here's something that might have been forgotten by us readers. What happened to them thanks to Bakuda.
Brian, Lisa, and Alec were going to die if not for Joe and his Nanomachines from Generator Rex being able to heal them. Alec was already the most screwed up and is still recovering from it thanks to the healing done to his brain. He's still trying to get use to having all of these emotions being less muted that it is influencing him.
Brian and Lisa though are traumatized and they're method of handling it seems to be focusing on other things. Brian on the Undersiders image and position as the "leader" and Lisa on how to handle Coil and Joe. This could just be their way of coping from going through what they did. Lisa was fused into the locker along with whatever was in it and Brian was spatial spread across another. And it has only been about a week since that has happened in story.
People that have been traumitized are not people that I would want to give advance tech to or leave on a moon base.
Also keep in mind the fact that we don't see everything! We are literally given small bits that aren't focused on Joe and the Celestial Forge showing the impact of his actions. Every time we have see the Undersiders it has been either in contact of the current "Mad Scientist that has exponential growth that does not seem to end" or in their interactions with each other involving the after math of Joe's actions.
We do not have reliable information about them outside of what Joe has along with tidbits to make a opinion about them.
I can't say much about Rachel since we haven't seen much interactions that were personal outside of Undersider meetings, including the one where she had her dogs attack him.
Alec though has talked personally with Joe and has been very up front with him. He's been honest about his desires and issues to the guy. Such as asking about if Joe healing him did anything to mess with his brain. A fact that is going to be shown during the next chapter I do believe.
Oh, and about how far he can throw them. Without including Reinforcement, Tetra, Ki, Aura, Mantra, Biotics, power armor, and any other form of enhancement I'm pretty sure Joe's base physical abilities are in the area of a Brute rating just from the combination of being a Greek Demi-God and Kenichi level Master. A level that allowed them to fight tanks and win.
And what he said.
