Some 2.5 year olds can handle restaurants, but plenty can’t. Pandemic toddlers, in particular, seem to have a very difficult time in restaurants because they didn’t get much practice early on. An infant will just sleep most for the most of the meal.
I understand your feelings, but I think you’re projecting feelings on a toddler who couldn’t care less. I think it’s nice and a really kind gift from you to give mom a special day where she can actually relax and enjoy her meal. She won’t be able to do either with a toddler en tow.
There are plenty of big family holidays to celebrate. Why not let mom have a relaxing outing on her own special day? Especially considering GD isn’t old enough to understand or feel left out?