This is nothing to do with getting involved in a new relationship. Quite obviously neither side of a separated couple need ask their ex's permission to become involved with someone new.
What both parties should do however, is consider the logistical and very real financial impact (for many households) any subsequent move may have. Not to mention the impact upon the relationship between the children and the non resident children - as, with the best will in the world, and like it or not, if you create a significant physical distance between parent and child there has to be a lot of damned hard work thereafter in order to sustain the relationship - simply because it's now more or less impossible to see the children on an ad hoc or frequent basis.
Yes ..... life isn't always black and white and sometimes - obviously - moves can't be avoided. The considerate, humane and decent thing to do in those situations however is for ALL parties to work together and come up with a plan that'll minimise the impact upon the non-res parent/child relationship, minimise additional expense (especially for non-res parent's household who usually have very little say over such moves), minimise time spent travelling to see/collect/return children, e.g. by BOTH parents sharing driving and meeting halfway. Arguably, if one parent decides - unilaterally - without any attempt at discussion and compromise - that parent should, morally, IMO, share even more of the inconvenience/expense which arises as a result of their unilateral decision.
My partner's ex certainly didn't do this - well, she lied and told him she'd do all she could to ensure him seeing his kids wouldn't be affected by the huge distance she created (unnecessarily) .... and then turned round and refused to budge her lazy backside one inch down the road. And it doesn't sound as if the OP's DP's ex even tried to pretend that she gave a damn about the move and its impact.
This isn't about minor annoyance ....
.... this is about real and significant impact upon your household where you have no choice in the matter, not to mention of course the potential for broken relationships which wither away because some households simply can't scrape together the funds required to continue seeing their non-res kids on any meaningful and regular basis (as perhaps suggested by Stepmooster's post). Imagine that you're counting every last £ and suddenly you're told that your household monthly income from next month and indefinitely for more than a decade is going to be at least £200 short - many many households would struggle with that and will invariably have to cut back on food and clothing (let alone anything treat like) as when you're up against it, you're usually less able to cut back on housing, utilities, commuting, council tax, child maintenance (obviously, before I'm burnt at the stake). That is what it was and still is like for us - and I won't apologise for feeling furious about it. There are other hidden costs too ....... the OP mentioned her DP's working hours would be curtailed if he had to spend extra time travelling - so you have a double whammy right there - additional travel costs and loss of earnings. Similarly, because I used to work evenings and weekends my ability to earn was also affected when DP had to set off on a 5 hour round trip (twice in a weekend). However much you want to see the stepkids, however much you love them, fact is if there's no money there, there's no money there and these sorts of situations aren't about a bit of inconvenience but can be about real ongoing financial struggle - through no fault of your own, and due to something you had no say in or any control over.
What I'm saying is that the parent with care has a moral duty in all of this. Most parents with care want their children to sustain a happy loving relationship with their absent parent - and would therefore only move if it really was unavoidable. And when it is genuinely unavoidable (I get that sometimes it is clearly) you then do all you can to assist in maintaining contact. Anything else is bloody selfish and arrogant - and believe me, in my own experience, and that of several other stepmothers I've known for quite some years, such a move is often used to try and prevent continued regular contact by some selfish exes who aren't stupid and who appreciate full well they're making contact extra hard.
BTW I was the mother of a stepchild long before I became a stepmother myself and encountered the sort of spiteful selfish gameplaying which I previously thought only existed in soaps. My ex actually moved about 60 miles away after we split - but it was with my full knowledge - and we both discussed this all the way. He had to move for work - which you can't argue with - but we both brokered a plan to minimise the impact upon our child, and the financial impact on me. My ex was more than willing to travel back to collect our child - but I preferred to drive them up to him at the start of contact so they weren't getting to bed too late .... in recognition of this effort my ex would reimburse my petrol - fair enough - but my main concern had been our child. We regularly discussed what was fair and reasonable, and if our child would be affected or not - surely to god that's not unreasonable. I have a very very low opinion of DP's ex who refuses to do the same, to put herself "out" (as she sees it) just to be spiteful, even though she created the damn situation - she doesn't give a damn about the very real repercussions of her decisions, and as far as she, specifically is concerned, actually seems to revel in causing us as much inconvenience and expense as she can by being as awkward as possible about contact arrangements (just to add insult to injury).
I know I've gone on but in a nutshell - when you're a parent and if you care about the relationship your child(ren) has with their other parent you simply don't make major decisions without the courtesy of discussion and co-operation, assuming you have a conscience that is. Is that really so bloody difficult to comprehend ?
Otherwise you have the situation I'm living with - that the OP is facing, and which several other posters are also experiencing. "Inconvenience" doesn't even begin to cover it. It wouldn't be right even if the non-res household was rich (though having plenty of disposable income would I suppose make it more bearable) but unilateral and selfish decisions like this can have a horrendous effect upon households which aren't so fortunate - remember too that the resulting lack of money also impacts upon the non-res children as they will also be affected by the lack of days out, holidays etc at the non-res parent's home. When the ex won't even deign to discuss any of it with you it just makes you feel like the lowest of the low ....... and the non-res household is very often placed under huge pressure to meet contact costs, regardless of how affordable they really are, because it is such an emotive subject. Without question, our household has suffered, and our youngest child has also had to go without because we have had this selfish expense imposed upon us for years. We are also painted as villains who "don't care" (to the children - by the ex) on the occasions we have been unable to use a full day's holiday required for a school play or sports day and have had to miss them. Any normal parent would explain how annual leave is saved up for school holidays but the distance makes it near impossible to do more casual things without using up annual leave.
OP ..... I'm very sorry to have somewhat hijacked your thread. You have my full sympathies and I just hope your ex is more reasonable and co-operative about this that our was/is. My blood just boils when I see (some) people dismissing this sort of situation as if a mother's wants should always override absolutely everything else regardless - even if it has a negative impact on her own kids. All it should take is honesty, consideration, discussion, compromise ......