I moved mum into a brand new facility literally 5 minute drive from me. I am the one that runs around for her, visit 3-4 times a week taking her out for two of those days and l look after all finances. My sibling and two of her friends live about 1 hour drive away but close to where mum used to live.
Even when mum was home my sibling would only visit once a fortnight for max 1 hour. Her friends would drop in maybe once a week to check in on her. I did the right thing and looked at facilities near them but they were old tired and awful. It has taken mum 17 months to finally settle and she says she likes where she is and loves the staff. They make me feel guilty ‘can’t visit every week too far to drive’ ‘didn’t realise how close she is to me.’ Sibling is always too busy and visits maybe once every 2 weeks. Mum never sees her grandkids as they are all older now with their own lives. Sibling asked if I would be moving her - I said not just to make it easier for you! Am I being selfish??
If your sibling wants your mom moved closer (which she doesn't, she just wants to assuage her guilt) and is prepared to do all the planning and will be happy to take over all the visiting, taking mom out for appointments, etc, then let her have her way.
You? Don't lift a finger. You've done exactly what was best for your mother!