Your girl makes an issue out of something so small? No disrespect to your girl but im convinced something is wrong with these women in general. I remember one time my little sister hit her head when my mother was opening the fridge, and im there comforting her while she is about to cry and i have the ice in my hand and im placing it on her head asking her which part of specifically.....
then my mom starts spazzing out like some maniac talking about how im___ years old and leave me alone with my daughter!!!
Because apparently you can't even comfort your own flesh and blood nowadays
Anyway as for thoughts on what your method was man....you were thisclose to doing it perfectly but peep this you made one big error and im not sure but maybe you noticed it already:
Me: Cool.
Don't text my phone anymore
^Remember in situtations with kids you have to be extra careful. That 'Dont' text my phone anymore" could be very damaging....especially with how vindictive women can be. She could use that against you in the future with your family, her family, her friends,etc. Heck she could even bring it up 30 years from now whether or not you are still together about how you told her that you dont want "Her or your daughter to contact you ever again".
We all know talking in person or over the phone can be a bit more effective sometimes. But i understand sometimes because of our situation we can only text at that specific moment. And it may be better in some cases like that because you wont have them play one of those "games" where they love to hang up while your still talking.
That "COOL" could have also been replaced with an "okay".
Because "okay" is a more arbitrary word and i would recommend it as a word to get used to using when in situations like this with women....Whether you are saying "okay" through texting or in person.
When "cool" is used alot of women would usually take it for you being a big smart ass to them.