Do I need to invite my sister whenever I meet our mother for coffee?

My sister saw a photo of Mum and me at a cafe and messaged, "An invite would have been nice." I'd gone into town to pick up a parcel. Mum was nearby, so we met for an hour. It hadn't been planned as a family outing.

My sister says she keeps hearing about things after they've happened. Mum and I do sometimes meet alone because our schedules line up, while my sister usually joins the larger family dinners. I hadn't thought much about that difference until she pointed it out. She also lives farther away, so a last-minute invitation often wouldn't work.

I suggested she arrange something with Mum too. She heard that as me saying the situation was her own fault. Now she wants us to put any coffee plans in the family chat, even if we know she probably can't come.

I'd like my sister to feel welcome. I also like having a conversation with Mum that doesn't automatically become a group plan. How would you respond without making time alone sound like a prize we're competing for?