DH just called the school district
to see what the criteria would be and the process if someone such as BM would attempt to register their child for the next grade when the previous school was going to retain the student. According to the school district, they would put SD in kindergarten again because that is what her report card and file dictates. After school starts, a conversation can be had with the principal of the school to see what the options are, but only in special circumstances would they complete an evaluation and move a child up a grade when the outgoing school of the transfer student decided the student would be retained.
The good news is that this washes our hands of a battle with BM because when DH and I just overlooked the curriculum and the standards at the end of kindergarten, SD still doesn't meet SD's new district's standards, it is more advanced. Now all DH plans to do is upload the outgoing assessment from the tutor on Thursday and then tell BM to keep DH informed on how registration day goes on August 1.