AITA for shouting at my ex in front of my daughters?

I (37M) have three girls; 8, 10, and 12. Their mother walked out on us for another man when our youngest was around 4. My ex still stays in contact, though, and pays child support.

A few weeks ago while doing laundry, I saw red spots on my oldest's underwear. I asked her if she knew about it, and she cried and told me she tried to call her mom, but my ex didn't call back. She'd been stuffing toilet paper in her underwear, hoping that would work. I explained to her that periods are nothing to be ashamed of, and found some great resources online for us to review together. I took her to the store to pick out brands of feminine products she wanted to use (she picked Playtex Sport because she's a gymnast).

After we were done, I decided I should do the same thing with my other two. My 12yo volunteered to be part of preparing them, and we made a whole night of it; it was wonderful, and I learned a lot. I even learned what a menstrual cup is, and how they benefit the environment.

The other day, my ex called back. I'll usually arrange a video chat and leave the room so they can have some alone time, and when they're done chatting, I'll come back in to talk boring co-parenting stuff like school, bills, etc. This last time, my ex was FURIOUS with me for talking about periods with the girls. She shouted at me that I was sick and perverted, why didn't I call her myself if I knew it was so urgent, I could've called one of their grandmas/aunts, but my mom has dementia, while her mom and sisters call me a loser because I teach kindergarten, so I'm not fond of them.

My ex told me I was being immature and should have just toughed it out for the girls. This really pissed me off, so I shouted back that maybe if she wasn't such a deadbeat and answered her goddamned phone once in a while, she could have handled this. I brought up everything she does that hurts them; she hasn't been to a single soccer game, piano recital, or gymnastics meet in two years, every other weekend when they come home from her house, they go straight to their rooms, only to emerge hours later asking me why she loves her new husband more than them, and what did they do to make her leave. My ex responded by saying I should tell them it's not their fault I couldn't satisfy her, and I screamed "fuck you", and she just smirked and pointed behind me, saying "Look what you did"

When I turned around, my 8yo and 10yo were standing in the doorway crying. It broke my heart; I never shout, so I know I scared them. My 12yo stormed in and started screaming at her mom, and while I appreciate her sticking up for me, this is not a battle I want her fighting. My ex hung up before I could fully deescalate the situation, and let's just say the girls have been given free reign of the ice cream and limitless hours of video games, because I feel so bad. I even watched all the Twilight movies with them, so don't say I don't love them. But in this instance, AITA for shouting?

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