Your child is very young.
BUT as they get older, kids do get more mobile and busy and active and get more into things.
So you NEED to remember that.
Is your Mom's home... baby and safety proofed? Medications or dangerous objects up high? For example?
It is wise for you to wonder about this. A Grandparent's mobility and physical limitations due to age or health, is important to consider.
I know MANY grandparents... who tell me that they are too tired or have physical limitations or health problems... to watch their grandchildren... but they enjoy doing so.... but yet, it is hard for them and they simply don't have the energy or attention span to do so.
But they don't speak up about it, to the parents. Because then, they 'fear' about who will watch their Grandchild or if the parents will let them or not.
BUT... also, sometimes, a Grandparent will NOT tell you, if they are having a hard time with babysitting. Because, they do not want to seem feeble or incompetent about it. So they don't say anything.
So you need to gauge the situation.
My Mom, once... was washing the dishes. I was downstairs, my kids were upstairs. My son fell... (nothing serious fortunately), but my Mom didn't hear him. And he was upstairs where she was as well.
So that is one example. But a situation where the Grandparent was not alert to.... what was going on.
So, also listen to your gut instinct.
This is not a judgement about your Mom and her physical disability... but about common sense and per safety. For both your child.... and herself.
As you said, your Mom has "severe arthritis...."
My Grandma had bad Arthritis too. SHE could have gotten injured herself, just by walking down her own steps in her home.
And no, they do NOT have, quick reflexes.
And when/if an Elderly person falls.... they can get broken bones/hip, etc.
It is for their safety too.
Is your Mom's home... outfitted with guardrails, handrails, non-slip surfaces etc.? Since she has severe arthritis?
We did that when my late Dad... became physically feeble. We even outfitted his shower and bath, with hand rails, for example.