Awww…I’m sorry he’s spewing. They do that, especially as they’re getting what they “wanted”. Keep communications written like you’re doing. They also develop terrible memories. Having proof of what you told them is good.
Being stuck as the responsible parent is hard - but the rewards are great. Many with true 50:50 custody spend a lot of time missing their kids or worrying about their safety when in custody of their ex; so there are plusses to having them 90% of the time, even though it must be exhausting.
