Is she significantly younger than you or just younger in general? She could just be a bit immature and not having kids herself you could just block that out and mark it off as her not understanding yet. I have sent my kids to daycare and for very short periods of time and they don’t get undivided attention like you would think. What you’re doing I think is the best option, especially if you are taking him places and teaching him different things.
It is natural for your sister to want her work to feel important, and it is to the people who rely on it, it just isn't for you. I wouldn't put a whole lot of weight into her comments. She won't even make them to your face! (She knows better) You can ask your mom not to relay any comments like this in the future. She's already on your side. It's good that the kids in your sister's care are happy and having fun, she just needs to remember it doesn't say anything about the experience your kid or any other kid is having.
This sounds soooo similar to my sister, she always commented on things negatively but would talk shit about my mom, except my mom would say she backed me up when she actually never did but just acted dumb, innocent and concerned lol. I definitely think you should address what she's said to your mother and if your mom has a problem with it, tell your mom to stop telling you the shit she's saying otherwise you'll be addressing it with her directly and saying it came from your mom. It sounds like your moms trying to pit you two against each other, this is what happened from my own experience anyway, not sure how your overall relationship is with your mother but I definitely think somethings being lost in translation for your mom to so comfortably tell you your sisters having all these concerns 🤷🏻♀️