Daddy needs to put his big boy pants on sharpish and man up.
Not sure at all why your daughters education should be expected to suffer?
Missing the odd day cos a half- sibling has been rushed to hospital with appendicitis is acceptable, making it a regular part of her upbringing is not only morally wrong, it may eventually get you into all sorts of trouble with the authorities.
Holidays- not sure what's wrong with camping? A holiday cottage costs the same to rent whether 8 people kip there or just 2. Butlins can be cheap if you collect newspaper tokens at the right time of year for a few weeks.
He just needs to adjust his vacation expectations from 5 star at the Taj Mahal to Bognor Regis to take into account the Kids HE CHOSE TO HAVE! Not many families with four kids manage long haul flights & disney world iykwim.
Not sure either why your kids have to be dragged here there and everywhere, each and every time he visits the twins. Yes, as siblings they need the opportunity to form a relationship, but lets face it the one year old is hardly ready to discuss the intricacies of pokemon just yet.
The 6 year old being closer in age should be included whenever it's sensible methinks, within reason - if the drive back means she's not in her bed till midnight on a school night for example his plans need adjusting. He needs to understand that sometimes the kids who don't have access to him living in their home daily may NEED a little individual emotional support from their Dad away from your 6 year old if they aren't to get jealous. This probably be will more of an issue once the hormones of adolescence kick in, but even at 6 & 7 they can get bullied at school, be scared of giving a talk to their class etc.
He also can't play the together card as a way of YOU winding up doing the bulk of the real childcare (snotty noses, feeding etc ya know the boring bits) when his twins are around. They are his kids not yours and they have a Mum they love very much, he is the parent and needs to give them proper attention. (Not saying you aren't and shouldn't be supportive, just that from what I've seen of life, kind dumped upon step Mums are being set up to fail through no fault of their own iywim).
Seriously unimpressed, he comes across as bone idle. In your shoes I'd be squirreling away a little secret savings account of my own. if he can neglect his first born kids, you have NO guarantee your own won't be in a similar position one day.