Congratulations!
I’m a mother to an almost two year; I sometimes comes here for advice and perspective.
My mother in law was very much at odds with us when it came to her expectations about “helping” and how much she would be visiting. She was expecting a lot more than we were comfortable with.
It says a lot that you have taken the time to read up (and realize their needs arent personal against you), are trying to be respectful of their space, and want to word things correctly.
I wouldn’t overthink what you’re writing, but I would try to manage your expectations of how often to visit and what those visits look like. I would also try to not make comparisons about who you think will have a stronger bond with this new bundle of joy. It’s not a contest and it’s unlikely an infant is truly going to bond with anyone besides their primary caretakers. Most of the time, that’s mom and dad. I assure you that if you’re visiting more than once a month, you will grow a strong bond with your grandchild. If anything, allowing a healthy little bit of space can create the air relationships need to breathe and flourish.
Each growing family is going to vary in their need for help, as well as space or time together. For me, weekly visits were the most I could comfortably manage. I would’ve preferred once every other week, but my MIL actually wanted to visit multiple times a week. So once a week (twice max) was our compromise.
Please also understand that not every new family wants help, and try to recognize what you consider help maybe not be considered help to them. My mother in law viewed her helping role as coming here, holding my newborn the entire time, telling me to go do something else, and resisting giving my child back when he fussed or we wanted to nurse. She also constantly gave unsolicited advice and comments about feeding, what she did differently with her own children when they were babies, why she thought current guidelines were silly, etc. True help for us would’ve been asking us to text a grocery list or bringing our favorite takeout so we could focus on our child. Grandparents are NOT servants and under no obligation to help with household chores, but if asked, many parents would welcome help with emptying the diaper bin, folding laundry or emptying the dishwasher. Those were simple chores that we often found ourselves weighing against a few minutes of sleep.
What you’re describing sounds more like a visit, so I’d phrase it as such. Everyone is different, but I actually would’ve preferred a text saying, “How are you all doing? Would it be okay for me to visit on x day for a couple hours?” rather than constant calls and texts saying, “I can come help!” when I knew her definition of help was the opposite of what we needed or were comfortable with.
Don’t forget that this is a marathon and not a sprint. Your grandchild won’t remember these first years, but they will remember the memories you build in later years.