Really need help with my relationship

I have 3 children with my ex, and am now with a new partner. My ex sees the children everyother weekend which is what he agreed on but he doesn't ever give me a time of when there back and will sometimes text and say he's not having them at all because he's choosing to work instead. My new partner gets really angry about this and has suggested that I stop the ex seeing the kids until he can give me a written agreement of arrangements so the kids aren't being messed around and there's consistency in their lives. My new partner has a child with his ex but doesn't get to see her because his ex refuses to let this happen. I don't want to stop my kids seeing their dad but my partner gets into a range if I don't agree with him slams doors shouts at me and just makes me feel like uv gone against him by allowing them to go even though there dad is unreliable. I've agreed to see a solicitor so his access is down in writing but have still allowed the children to go until this happens because I don't want them to miss out. It really pisses me off when he lets them down or when I'm waiting around for hours for them to be dropped off. My partner flies into a rage if I don't do things his way and agree with what he says. This happens everyother weekend and I'm left feeling like shite because of his mood

Your ex is unreliable & it isn't fair to any of you.
Glad you're meeting with a solicitor to settle things.
That being said, it isn't fair for your current partner to put you in the middle.
He sounds selfish, immature, has anger issues bordering on abuse.
Your kids don't need to be around this either, not a good male model.
Is this someone you're really sure about having a long term relationship with?
Sorry to be blunt, it's the kids this is harming the most.
Wish you the best.

He does have anger issues and he's trying to get help without much success to be fair getting passed from doctor to mental health and then back again. I don't ever let the kids here anything and we never say a bad word about there dad in front of them. My partners anger flares up to the point he's unable to control it and he normally takes himself off. And then when he's calmed down he understands he was out of line. He also suffers with major depression and anxiety, he became worse wen he stopped taking his tablets about 6 months ago, but he has now decided to go back on tablets because it's not fair on the people around him having to suffer. Just hoping they giv him a bit of a lift to seek out therapy as well