Yikes! Need help, please.

[TrentC]

The downside is, he knows I always have my cell phone on me. I get tons of texts a day. He is going to think ignoring them is game playing.

Well, it sounds like you're a busy woman; let that be your excuse.

"I'm sorry, I was at lunch with so-and-so."
"I was making lunch for the kids. What's up?"

If he thinks you're game-playing, point out that your life got a lot more complicated when he walked out.

I'm thinking it might be better to not initiate texts, but I should respond?

The only texts you should be initiating should have to do with his responsibility to the kids. Picking them up, dropping then off, schedule changes, etc.