But what is it that you are afraid of?
Doesn't matter. Makes no difference whatsoever. The OP is uncomfortable with unsupervised contact. No justification necessary.
Allow your child to be loved, unless you have valid reasons not to.
No one is stopping the aunt and uncle loving the child. They're not being denied a relationship with the child; merely unsupervised contact. My DB is never left alone with my DC - much as it grieves me to take this position - because he has an alcohol problem. As a parent, I/we judge that this makes him an unsuitable person to have sole care of a young child. Protecting the DC is our job; we'd be failing as parents otherwise and DB fully understands. Still doesn't mean DC and DB don't have a fantastic, fulfilling, mutually-beneficial relationship. I don't understand your point.
Your vague feelings of anxiety seem to be about what you need more than what your child needs.
I can see no basis whatsoever for this comment from what OP has posted. If this SiL + DP are unable to love the child unconditionally, no matter what the terms of contact, I'd suggest the OP's instincts are spot on and the in-laws are the ones with a problem.
What better way to do that than in the relative safety of leaving them with a family member.
She does so (with the PiL), as she's previously made clear. Just not this particular family member.