I have jury trial rights in regards to an eviction but not in regards to legal rights to my child?

That’s right, in fact you need to waive them before your landlord can evict you and most renters waive those rights unknowingly. In regards to keeping legal rights of your child? Every parent who has requested a jury, as a last desperate attempt to keep legal rights of their child(ren), has been denied this option by their judge. Thus a parent’s request for a jury is “a barren one” and every California judge, in every one of these courts that takes legal rights/custody of a child from a parent has denied it and will continue to deny it.