It is hard, as someone caring for others, to accept outside intervention. From the perspective of a Carer, that's my opinion.
After 15 years of Caring, I am finally having to accept outside help. It is a bloody horrible thing to have to do, admit you can't cope with your current situation without the help of strangers. And I've only got to that point because my family has hit crisis point with my toddler being dxd with SN's and medical needs as well as myself and two of my three older DC.
Maybe your DSC's mother hasn't hit that rock bottom place yet? Maybe her asking you to vary the court order IS her having hit tock bottom. If you think about it, (I know your back story), this woman would seemingly blend her own eyeballs before asking your DP for help. Yet here she is, admitting (albeit through actions, not the words she is saying) that she CAN'T cope without his help...
I know it will be exceedingly difficult to be magnanimous towards your DSC's mother, given the prior history, but I see this as her roundabout admission that she DOES need your DP's help.
Ultimately, your DP holds all the cards. He has the choice whether to stick to the court order currently in place, or to go with her demand / request (depending on your POV). Ultimately he needs to decide whether the effects on his DS are worth adhering to the court order.
Facts are : Your DP's Ex has to work to keep a home over their heads. She works FT.
She has an elderly mother requiring care.
Summer Holiday care is very expensive, and may be outside her budget.
Lots of people care for their younger siblings while their parents are at work, and elderly relatives, without outside 'help' - which the Grandmother, btw, is quite within her rights to refuse herself, and may have done so, expecting her DD to care for her rather than strangers.
Therefore, your DP's Ex has arranged a combination of care of your DSS by his older sister and GM, to enable her to work.
Your DP 'is happy to arrange his work around increased contact with his DC's'.
So. These are the facts.
Could you maybe try to see this as her actions ASKING your DP for help, as deep down she knows the situation is not the right environment for your DSS, and she thinks he would be better with his dad than his GM. Just because she won't say that out loud, doesn't mean that that isn't what is happening!