"Early this year the whole family moved to the State I live in as my brother got a transfer with work, they now live 1.5 hours away from us. He now has a 3 year old which my parents absolutely adore and dote on who I have never met."
Your brother got a transfer - and your parents up-sticked and moved with him? And your "sister who still lives with them." If your brother now has a three year old, he presumably has a wife/partner, does he live with wife/partner or does he also still live with your parents?
Whether he does or not, that's a weird dynamic, that they will tag along with his job move. And if his employer moves him again, will they follow again? (I'm pretty sure the answer is yes.) Can you see how odd that is? To move from your home town, all your friends, all your other relatives, maybe your jobs, from the home you built and all the memories that it houses - to walk away from all that because one of your offspring's employer moved them (possibly temporarily) to another location? When offspring moving away is pretty inevitable these days?
It sounds suspiciously as if your brother is The Golden Child, which makes you The Scapegoat.
When other Mumsnetters have described this dynamic in their own lives, I have been struck by usually how little the Golden Child cares about the parents, and how desperately the Scapegoat seeks some crumb of affection from them
. There's definitely that sense from you, of reaching out, your broken heart.
So I'm going to go out on a limb here and propose that your brother really doesn't give a stuff about your parents. That in his eyes they exist merely to supply him with 'stuff', be that stuff money, time, adoration childcare, whatever. They are not people to him, just acolytes / servants / skivvies / a resource.
And maybe their tagging along with his move, he finds annoying. Their presence gets in the way of his grand new life and lifestyle. Or maybe they're not as good at providing any more, they might even be becoming a bit demanding. Getting on a bit, needing a bit of looking after themselves, maybe? However it's playing out for him and them, I would be deeply suspicious of their motivation in contacting you, because in my opinion they are only doing it because they want something. And they expect you to comply.
The other part of my brain tells me that my parents are getting old and this may be my last opportunity to forge some kind of connection with them. I don't want to have regrets when they go thinking of all the what if's.
That part of your brain is the part that is still seeking the crumb of affection from them. Because that's what they trained you to do, all through your life until they cut you off. Please don't kid yourself, there will be no forging of any kind of connection that would be healthy for you. They will treat you as they always have - The Scapegoat.
Please, protect yourself and your children from this ugly, damaging pair. And from your brother and sister, who play along with them because it suits them to do so. Please consider what regrets you would have when they wreak their havoc on your children as they did to you for all those years. There are no 'what ifs' because they have not changed. It's possible they'd pay some lip service to reel you in, but your parents are incapable of anything more.
Please, protect yourself from your poisonous family, and tell them no. It absolutely is "ok to say thanks but no thanks".