The only way to possibly even this up is, in the absence of your older child’s father, to consider adoption? The GPs may still treat them differently, but at least then your DP would be in a position to take them up on it.
Sadly people generally don’t look upon step children as family - I ws raised from the age of 3/4 by my step father, with whom my mother had two more children. They had a messy divorce and I distanced myself while at university. Afterwards I reconnected because I loved my (half-) sisters and step dad who always made a big song and dance over the fact that he loved me and thought of me as his own. When lock down happened contact became limited and it has take me the last five years and DSD’s 70th to realise that’s not really true. It’s a story they all, half sisters included, tell themselves because to consider themselves so cold as to not feel about me - and more importantly my kids - the way they feel about each other. My kids have autism/ADHD needs - so do both my sisters and a recent half brother my a later marriage. I assumed they’d be there, that they’d care, that they’d want to support us. Zilch. No calls, texts, recognition of birthdays and exam milestones. They simply do not give a fuck unless they need numbers for a family birthday BBQ. They won’t acknowledge it, but I went NC in August and had one text from one of my half sisters.
Am heartbroken as I realise that I have always been trying to be good enough - doing degrees (and currently a PhD) because they are highly educated professionals and I wanted to be deemed worthy. But I am done with the lot of them as noone was there when my eldest was having a breakdown and not a single one of them checked in on my son after GCSEs this year. I don’t need them.
so, I would accept that unless your DP formally assumes the father role with adoption (mine didn’t) you have no power to insist your eldest is treated the same. And in that case, you need to do a lot of work to ensure her self esteem is strengthened and not linked to the step family. And then, because your youngest may not understand your protective stance, you will need to work on your relationship with your youngest to ensure she does not feel you love your oldest more. As I grow older I have come to realise blended families really don’t work out like the Brady bunch (in fact neither do non blended families), all you can do is be vigilant and expose them to opportunities to build their self esteem independently of you, your DP and his family.