Mom went to the hospital for 3 days. Now the nursing home wants to have me sign a re-admission form. How will this affect the 90 day wait?

My mother had a stroke on a Tuesday, was released from the hospital on a Friday of the same week back to the same room at the same nursing home where she resides. Now the nursing home that already confirmed they would hold her room until she returned wants me to sign a re-admission form. Then they changed it from a re-admission but stating it was a leave of absence. How will this affect the 90 day wait for the secondary LTC insurance after Medicare to pay when she had just got to the 90 day wait right before she went into the hospital? If I make a mistake signing this it will cost us about $7200 since the 2nd insurance doesn't pay well (only $80) per day out of $269 but it is still $7200 lost if I make a mistake signing. When I first asked the billing specialist about this she claimed she had no idea. She knows every in and out of billing as she is the finance manager. So I am sceptical.