Very very similar to posts by new partners...
What evidence do you actually have beyond what your dad tells you and odd comments from and rare contact with your half siblings that there's even neglect let alone worse?
3 dc with a year or less gap between each child - how old were they when your dad and his ex split? If they were ever properly together (the way you word it suggests they possibly weren't)
Cos that's bloody hard work for a single mum even at the ages they are now!
The eldest has a disability which, let me tell you as the mother of a disabled child myself is bloody hard to get dx/treated/adjustments for!
My brother was a daddies boy when he was younger and my dad used to take him to football etc smacks of at least a little Disney dadding to me
Conversely
My dad and his wife have rules such as no phones at dinner table, no phones after 8:30pm, have veg with dinner and family time including a dog walk or similar every time they have them for a weekend is how they parent
Makes me wonder if your dad and his wife have dc of their own? There seems an odd mix of "Disney parenting" mixed with possibly over prescriptive parenting in other ways.
Gradually the weekends stopped, my brother is addicted to PlayStation and plays from 3pm to 4-6am
How would you know this for certain? Seeing as you're never there?
The eldest hasn't been to school for 4 years and is not home schooled again how do you know this?
The anxiety issues do need addressing but aren't necessarily purely learned behaviour if their mum is anxious type then genetics may play a part too.
She cooks my brother chicken nuggets for breakfast cos it's all he will eat
1 it's better than him having nothing - which happens in a LOT of households and ss would definitely not consider an issue. At one point I was very ill myself (has a breakdown so I absolutely DO understand depression - and anxiety I have dx ocd) and giving dd some "unusual" things for breakfast. I had some ss support among others at the time and "confessed" and they didn't bat an eye!
2 clearly she is aware that breakfast is important and is dealing with it as best she can
My Dad used to have them every other weekend and see them 2 nights a week, now she's moved them 100 miles away to be nearer her family. and? How old were the dc when they moved? Your dad could still see them at weekends and even in school holidays, he could have gone to court to get a contact order - why hasn't he?
Re their not wanting to come Boxing Day, around this age is when going to a nrp becomes a bit boring and a chore, it was up to him to have developed a closer relationship with them BEFORE now so they didn't feel like that so much AND to make it fun (without being Disney) for them
Stepmum text middle sister and she replied "well dad never bothered coming to our school plays etc" which are definitely not her words
What makes you think not her words? My dd would, could and did say pretty much the same to her dad around the same age without any prompting or influence from me!
My dad has always worked full time but is the most caring, loving, funny Dad, she would tell him about parents evenings and school plays the day before so she knew he wouldn't be able to book the hours off work.
Yep! Typical attitude from supporters of passive, lazy nrps!
She is NOT his secretary! He could easily have asked the school/kids clubs etc to ALSO keep him informed on key events, my dd is almost 20 and at the age your half siblings and even the latter parts of primary school so coming on 15 years ago most if not all schools had their diaries easily and publicly available online so in all likelihood he didn't even NEED to ask the school to email or post to him dates and times of parents evenings etc he could have simply looked on the schools website.
NOTHING you have said is especially concerning aside possibly from the anxiety/phobias (and there's a huge general increase in this among kids of this age especially this year!) and I suspect from the mother achieving dx etc that they ARE regularly seeing hcps who will have training, knowledge and objectivity that YOU so clearly don't!
I don't think you're concerned particularly for their welfare, I think you're more concerned about your dads lack of contact etc and are blaming that solely on their mother when he has done sod all in how many years to address this?
he's just got very depressed about this that he hasn't got the push to take it to court
There's always excuses by nrps/their supporters.
He hasn't always been this old (he'd have been 38 when the eldest was born and 40 the youngest?
You need to stop excusing your dad in this
Exactly!
but to me it looks like you have your dad on a pedestal, an agenda against the mum, and that neither you or your dad really know these kids anymore so are assuming a lot.
That's what I'm seeing too
even though they split when my brother was 4 months old so she was single parenting a 2 year old 1 year old and a baby and SHE is the one in the wrong?! Not buying it!
My other concern is, she made allegations to my dad that her stepdad (the kids grandad) touched her as a child yet she's moved them 100 miles to be close to them
My dad also abused me, I moved after my divorce nearer to my parents and other family for the support. Doesn't mean I EVER put my dd at risk! She's never even been within 6 feet of my dad! When did she move there?
2 months - well if you were GENUINELY concerned about this you wouldn't have waited this long and nor would your dad and you wouldn't even be hesitating about calling ss, but I don't think you are genuine
Also means until just 2 months ago they WERE near enough to have proper contact and for your dad go easily attend school events and gymnastic shows etc...but he didn't!
but he's always worked 12 hour days including weekends to provide for them.
Excuses excuses excuses!
A telephone call, an email, checking the schools website takes MINUTES and aside from phone calls can be done any time of day!
He gives her a lot of money per month to feed and clothe them
And?
I'd LOVE to know how much! I'm guessing it's actually cms minimum if that and he begrudges it! Very unlikely to be close to the 50% of what it actually costs to raise them!
My Dad is no angel, he has his faults you don't say 
There's SO much more he could have done YEARS ago and chose not to. Kids aren't stupid and certainly by the time they're getting to early high school age they start working out this sort of stuff by themselves.
Were you raised by him? What does your mum think of him?
Something feels off and it's not necessarily your siblings mum!
Yes you can contact ss they're well used to fielding calls based on bias and misinformation but they're obligated then to at least investigate which puts stress on that resource and will cause stress to your siblings and their mother. Frankly I wouldn't be surprised to learn if there's already ss involvement FOR SUPPORT as she has 2 disabled and 3 anxious dc and is a single mum.
But I get the feeling you don't want her to get support, you want her to be officially criticised/admonished in some way, found lacking - that isn't generally how it works!
Also v unlikely the children would be removed from her care and placed in your dads as there needs to be awful things happening to the dc for that to happen (unfortunately for the kids who are being genuinely neglected and abused!) which I think may be what you're hoping for - even though it honestly sounds like the last thing your dad would want.
Ss also don't negotiate the terms of nrp contact.
That's for the parents to sort out and if they can't then it goes to medication and if that doesn't work the courts.
This whole thread has made me feel VERY uncomfortable.
You really need to examine your motives op.