Does this not count when it’s a parent and a child?
Absolutely not in the way that it does for adults.
DTwins weren't up by the time DH went to work. He might catch them before bed tonight, but he's picking up something on the way home from work. So most likely won't. On the days he does get home in time, it will only be for half an hour. They go to bed by 7.
DH and I have a meal. We talk about our days. Put the TV on. Potter about. Take a cup of tea up to bed.
We as adults have some great quality time.
DTwins don't. Neither would any other child that was here. Mine, his, or the neighbours! They'd get quality time with just me.
DTwins see him at the weekends. The fact he lives here while they are asleep, does not equate to what we do at the weekends with them.
For OP, her DH and ex, by choosing to separate, accepted that there will be time with the DC in their homes, and time without. If they didn't accept that, they should have stuck together as one of those couples who are together just for the children. Because that's essentially what the husband is doing. I must dedicate no time to my new partner and child without bringing my other child along, one child must be present at all times my partner wishes to spend social time together with another child. SDC can have one to one time with me, as I take them to hobbies and dinner. My other DC? Zero one to one. Not even a walk to the park. Think of the poor SDC having to accept he does the same for DC. Imagine if they thought this child was equal to them.
He made his decision to leave the ex and child. OP started a family with someone who had a DC 50% resident. He's now changing that to 50% resident plus 100% of social time, and for some reason, the ex doesn't mind the child she already doesn't have for half of his life, leaving her even more.
The DH is so far in the wrong here. He is massively disregarding his own child, then gaslighting OP that it's her not liking the other.