@candlesandpitchforks
Let's get a few things straight.
The mum is under no obligation to change her dates/times etc. She should be willing to oblige but she doesn't require to facilitate. Why on Earth should she care about the OP's kid?
She is ZERO connection to the new crown Prince.
The OP is the mum to new child & of course it's understandable that she wants the party on the actual day.
BUT the child is too young to know.
She is also Step mum to her dh jids. So there is a relationship that requires nurturing & compromise & she should be wanting to nourish the relationship between her child & their siblings. It's good for her dc to have that relationship. It's healthy.
DH should go pick his other kids up the night before or early morning of the party or OP should change until following week.
On this one occasion as baby too young to know. In future years I wouldn't be so flexible. But also in future years the dc may want his siblings at his party & they may have to change things to suit.
Best to all get on. However the OP unwillingness to do anything whatsoever to compromise is appalling & the DH unwillingness to make sure all 3 of his kids are a priority is appalling.
None of this bodes well for this relationship.
It's up to OP & her DH to care for their blended family of 3 kids.
Not the ex wife's monkeys & not her circus.
And I'm a step mother with challenging step kids & a partner who can be an arse about it.
You're beyond wrong OP