OP I have two step children, one with PDA, two years ago I could’ve written your post.
It can and does get better I promise. Some tips from me:
Take up your place. It’s your home, your rules. Set your boundaries and expectations, be clear, keep it simple, but have authority. If dad doesn’t like it, he can leave. Let’s be honest he won’t because he has no balls!
If you have children with autism -and especially SALT, try a visual (pictorial) rewards chart. I used this to move us into good behaviour, or to ‘overcome’ things like encouraging them to do things for themselves. Incentivise with Robux/PlayStation voucher/whatever they are into.
If a kid has autism, shouting doesn’t always work. I’d really recommend you do some reading around it. Shouting can increase what they’re feeling on a sensory basis. So it can elicit a fight or flight response.
Times and rules are different in both houses - deal with it. That’s the message our kids get. With school travel and other pressures it’s tough - and that’s life. It’s a good lesson to learn.
Spend quality time with them - I promise you your attitude towards them will change if you actually like them. Art, swimming, parks, even sitting down for dinner. It changes how you think, they respond to it, they see you as a friend not a foe.
And finally - stop giving two hoots what BM thinks. What’s she going to do? If dad is on the birth certificate and she takes you to court, they won’t simply say ‘no dad can’t see the kids’. Courts are busy, they don’t like time wasting, they like to maintain the status quo. Unless the children are at risk of neglect I can practically guarantee it will go nowhere beyond formalising an agreement you already have in place. It’s a lot of time, effort and money.
This is symptomatic of living in the shadows because someone else - you think - has the power. They don’t.
If she wants to start court proceedings, good luck to her. But you MUST call out those threats not back down.
But your biggest problem is Dad guilt. Disney dad is symptomatic of someone who knows they did wrong. You must work dad through this to survive. Children need boundaries, rules, guidance. A new child presents you with the opportunity to start afresh with rules and boundaries - use it.