The extra info you added changes things a bit.
But, whenever a current partner mentions that her dp or dh pays child support (and then always seems to add it's more than CSA minimum) it feels like they kind of think that because he does what he actually should be anyway it means the ex owes him something be it more contact or just more respect etc.
I dunno if I'm wording it right, but him paying more than the basic minimum CSA say he should isn't noteworthy and I find it odd when people mention it, esp when talking about contact. Paying for their own children is a minimum requirment and shouldn't be an option, so when it's pointed out that they do, in a way of defending them or painting the ex in a bad way, I wonder what other normal things they do that they feel they should praise or the ex should be greatful for.
His job that takes him away a lot, was it one he took after the split? If afterwards then maybe the soliciter agreement needs rearranging anyway, especially as there's also extra children since it was made, there's ways he can do that without wrestling the DC away, he'd know that if he'd looked into it, but he needs to compromise too, if he's taken a job that means he sees his DC less and then gone on to have more children knowing that would reduce contact a bit more too he has to understand that it's a bit reasonable for her to be unhappy as it means she has to pick up his reduction is caring responsibilities and financial contribution. If she has to be thankful to him for contributing financially then maybe he can be thankful to her for providing the majority of care for his children for him for the majority of the time.
If he can't see them much due to work, then it's all the more reason for her to have a relationship with the DCs grandparents so that they still get to see them.
I'm not saying she's not unreasonable, but there's things your dh can do to sort out contact, and a bit of her bitterness and anger may come from some of the choices you making in your household having an impact on her and the kids, like having more DC meaning she has to make up the financial reduction, him working away limiting what jobs she can work as she has sole caring responsibilty. Not saying he needs her permission to have more DC but I can see why she'd be a bit cheesed off and usually the man can go on and make choices the mum can't, like working away, because he doesn't have the worries of having to physically look after his children and sort the childcare and school pickups and homework and PE kits etc etc. She's doing that for him.
And the way you describe your Inkawsinlwas relationship with her in the first post doesn't match how you describe it in the second. Perhaps they are not standing up to her for similar reasons your dh hasn't?