I think you’ll upset DD1 more than you realise if you go ahead with this and possibly damage your relationship.
My sister was outgoing, funny, and very loveable as a child. I was chubby, shy and awkward, I’m neurodivergent but wasn’t diagnosed until I was an adult. I had lots of problems with friendships whilst my sister was popular.
My mum was aware of my struggles and I suspect neurodivergent herself so was a great support but my dad made it clear he thought any issues were my own doing. They often argued about me, my dad thought I was just hard work but my mum used to defend me.
I had to spend my whole childhood being compared with my sister but it hurt the most from my dad, I could imagine him thinking like you and being happy to invite a friend for my sister knowing I’d be pushed aside.
When my sister had a daughter my dad doted on my niece, he paid for my sisters driving lessons, a car, her wedding and helped her buy a house. I struggled alone in the background, my mum tried to get him to see what he was doing but he didn’t want to see it. The final straw was when he took my sister and niece on a dream holiday and lied to me about it, my mum was so upset but it was paid for from my dads inheritance. I moved out at 18 and hardly saw my family.
My dad got cancer and I obviously cared but I was bitter and hurt too, I struggled with my emotions towards him.
We later lost my mum but for 3 years I’ve had no contact with my sister or her children after years of comparison and resentment towards her, I have never properly grieved for my dad because I’m still so full of anger towards him, I’m angry with my mum too for letting me be so pushed out.
I’m having therapy to try to work through some of the anger but I don’t think I’ll ever be able to forgive my parents.
My sister ended up being a spoilt entitled person who thinks she is better than everyone, my dad used to tell her she was.
I have posted about this before, it’s obviously a very extreme situation and might have no bearing to yours whatsoever, I just thought I’d share it in case any of it applies to you. Please don’t let your daughter feel like I do, I’m 40 years old and with no parents I’d love a close bond with my sister, if we hadn’t been played off against each other for years I think we’d have been a huge support to each other.
You risk a relationship with your DD1 but also risk her hating her sister, I (like other posters) have picked up on an element of your DD2 being the golden child, if that’s the case then it will cause resentment between your daughters.