Update and when or how often should we visit?

One thing I always did when my father was hospitalized was introduce myself to the staff nurses, provide contact info, and ask when would be the best time to call and get an update on Dad.  I did visit almost daily except when I was exhausted, so the staff knew I was involved.

You can also ask to meet the discharge planner who will handle the transfer, and professionally make it clear that you need to be notified when the transfer has been determined.  Staff sometimes don't provide enough lead time for transfers, especially when they're extremely busy (such as during the Covid months).  

In my experience, it's best to be at the SNF or rehab facility when the transfer is made, as it can be very confusing to the patient.

It's the hospital's responsibility (discharge planner), though, to provide the requisite medical information.   I also always asked to review this as oftentimes inappropriate meds were included as being necessary.  First thing I did was challenge any psychotropic drugs; Dad never needed them and I wasn't going to allow him to be drugged up.

 You will have to meet with the SNF admins, review (and I mean REVIEW entirely) all the intake documents.    That raises another issue; has your mother executed any powers of attorney giving you authority to sign for her?  If not, then she should sign for herself - it's a financial liability issue.  

What you can do is get together a wardrobe for her, pack and be ready to take it when Mom is transferred.   I made a checklist for myself as we dealt with so many rehab adventures.

As to visiting, I would go anyway for personal observation of your mother's status.   I would also bring and leave get well or thinking of you (as may be appropriate) cards to leave for her so she knows she's not alone.

Are you visiting while she is in the hospital? If so I would keep the same schedule.