cedric you've deliberately ignored the issue to air some completely random issue you clearly have which is unrelated.
The issue that the OP has is that when she talks to her step kids in a normal human way, their mum has some sort of aggressive go at her - not sure if it's directly or via the kids or her partner.
It sounds like it's become a bit distressing and out of control. It's not healthy for kids to be given the impression they're in charge and can control the grown ups via their mum, or the impression their mum rules the universe by virtue of other humans coming out of her foo foo. It's not helpful if your partner isn't backing you up, and tbh you sound a little depressed, and like you need a big hug and be told that you are valued.
I think, hard as it seems, just now you need to try to act 'normally' as you would with any other family members or friends kids. When inevitably things get fed back to you from whichever route you need to politely tell them that you are treating them like your own, and in your own home there are some rules which may be different to mums house but they are to be respected. If this is your partner feeding this back you need to tell him he's not the vessel of his ex and her parenting wishes, and if he wished to raise his kids exactly per his ex's house then respectfully he would still be living there so please back you up!
My partner roundly ignores his ex's pointless feedback about how she feels we should run our home, and I wouldn't want to be being told by some random stranger how to act within it. Realise that over and above being mean and confusing their kids, the kids mum has no power in your home, unless there's something so serious that she wishes to try to block contact with you (such as drug abuse which I presume you're clear ;-) )
To be honest I couldn't deal with it all if my situation was like this, where's the thanks? Being a step parent is hard enough, you start out inviting virtual strangers into your home, inevitably you end up changing your life and paying for them (6 years holidays in kids holiday camps anyone). Every now and then people need to realise that you didn't actually sign up for this in life, they're actually not your kids and actually say, thanks for that, thanks for being their for my kids and loving my kids you're great. I appreciate it very much when my partner says that, it's a nice thing.