Instead of trying to micromanage your responses or control your actions, become totally relaxed, enter a very good state where you are FEELING GOOD and operating on the level of feeling good, not on thinking or micromanaging.
You want flow state. You want to be in state - and you won't get it through walking on eggshells trying to control everything.
I'm a dude (are you a woman?) but I make myself feel really good (if I'm not already), which turns off the mental commentary, then I just smile to myself and let my eyes go really relaxed. Then I approach whatever my body takes me. Think of it like your body is leading you. Think with your feeling, not with your mind.
This will eliminate your thoughts of being rude, of neediness for people, of needines for approval.
Imagine Tony Robbins in a crowd. Or Brad Pitt. Or...just maybe...imagine yourself being really awesome, feeling really good, just being totally relaxed and saying the first thing that comes to mind.
For it does not matter what you say. At all.
I've had to run after kids and watch them, too. If you're a fun person, they'll be more likely to stick to you
.
You don't have to imagine anything. Just feel really awesome, just incredible and then talk to the first person you feel in your view. You know that you WANT to talk to them, and by feeling good you are giving value and helping others feel good. You are naturally social.
This was detailed. The quick version is "The body demands expression," as in, whatever is in you DEMANDs expression, and who are you to deny the body? Hence you just talk to people.