@KeenHiker
Read your updates OP sorry you are no closer to resolution.
Firstly, if you went to Prep yourself you know precisely what you are asking your younger daughter to give up. Sometimes you can be lucky and have a really good state school, but mostly there is no comparison. If your husbands present or future neices/nephews are likely to go the private school route your daughter will end up misaligned to her cousins, and she will no doubt be aware at some point - either through her own intelligence or the family grapevine - that you and her sister were the reason behind her having a great opportunity taken away… which is going to place both you and DD1 in an even worse position than now.
Secondly, if you are working full time, feel so strongly that your elder daughter should receive the same treatment and have the precedent for 50:50 division of bills. Then you could consider funding your elder daughters education - which would be fair - and either working more/seek promotion or ask your DH to support more of the ‘essentials’ during the seven years of senior school. This may mean kissing goodbye to a car, fancy holidays and handbags, but if your daughter is your priority then it will be worth it. The majority of people I know have to compromise to send their children to private school. And splitting the fees between you seems fair. Remember there are bursaries and other means of support your daughter may be entitled to on the basis of her academic ability and/or absentee father.
You have been incredibly naïve to think that your elder daughter would not be aware of her sisters wealth - your younger daughter was always going to have massive financial advantage due to her family. And your elder is not a dimwit and would have sussed things out early on whenever she has nicer clothes, presents, activities etc bought for her and later obviously when her younger sister appears with a brand new car and is on the housing ladder years before her. Your husbands family will get gifts and things of course - but it will be token and polite.
Please do try to facilitate contact with your former partner’s family - this is the only way of your elder daughter having a sense of who she is and proper familial relationships. There is no compromise for that and it is more worthwhile pursuing than fabricating a mirage and trying to force your husbands family to step in as a sticking plaster - it’s all fake. Awful about your elder’s father, but make the best of it you can.
Regards the photo with Granny; it is a two minute photograph, the woman is very elderly and doing this will give a lot of joy to the people who will miss her when she is gone. Presuming most of the children pictured will have some of her wealth trickling down to them too…. So really it would be very inappropriate for your elder daughter to be included - she isn’t related to this woman.
My advice would be don’t destabilise your children any further by creating another broken home. Your DH does sound reasonable and has contributed to your elder daughter having a vastly better quality of life than she would have had if you hadn’t met him. He is prepared to step up and parent her and to contribute to her well being, but there are limitations as he is not her father - he is a step father. If you feel so strongly about your elder daughter also having a private school education then you need to pay for it and suck it up that you have to compromise to do this and ask for some support with day to day things from your husband for the time period.
Go to the wedding and get on with it. Accept the photo is going to happen and allow the grandmother some 1:1 time with your younger daughter. In about 10yrs or so whenever your husbands parents have passed or gone gaga you are really not going to have to worry about making accomodations regarding his family; they will all scatter to the wind. Don’t upset yourself about them. Also in 8yrs time your elder daughter is going to Uni so no point upsetting the apple cart - if she was 2 and you had another 16yrs of childhood left you’d have a point but this is really going to be beyond conversation in a flash when your daughter is an adult.
What you need to ascertain now, beyond the wedding and private school issue, is what other plans your husband has up his sleeve, be it with his own money, or using for example a trust fund set up for DD2. Because you need to prepare yourself and your elder daughter for this and work out ways to bolster her resilience and self esteem. Think big things - does he plan to pay for more expensive activities (horse riding/skiing) and school trips for DD2, gap year, all Uni fees + accom, car, wedding, house deposit, health insurance, is he contributing to an ISA for her for her 18th?
You need to find out all this now, because it does diverge your daughters paths somewhat. And he is well within his rights to want to do any one of those things for his own offspring but not feel responsible to do the same for DD1 because she isn’t his and he has not formally adopted her, nor has he any intention of doing so.