Excellent post, swing.
OP, your DP and you found out he was a dad just as you got together. You work as a solicitor, is this part time by the way, and will fit in with school pick ups or will DP do those or what?
The ex, the birth mum, she wasn't working til recently, and lived on benefits, and applied for maintenance from DH two years ago, that being the first he knew of his child?
All that must have been a shock. In it 'together', you and DP sound like you have launched yourselves into making the best of it you can, although DP is more tentative than you are.
As dad, your DP might be being more gentle and actually more sensitive to the ex , seeing the picture more in the round, more realistically and empathetically than you. But he is involving the court now. It's a shame that things have come to that. Now you are his highly qualified, litigious girlfriend, have you encouraged him to use the court system? Was it your DPs idea to offer to keep maintenance the same even if he did more overnights, and to agree this outside of CsA? It's a shame he sent a solitor letter. They are upsetting to receive. They come from a place of the other being demanding, entitled, arrogant, and accusing. Maybe the mum thinks you are behind this?
This infant child is likely to have a very, very close bond with his mum, and vice versa.
"With Mum and with Dad" are the best places for an infant to be. As step mum, you need to support this.
I would advise that, even though you mean so well, and you do loads of childcare, that you learn from these mumsnet responses and you take a deep breath, suck it up, and see that your intrusion into mothering and devaluing the birth mother of this boy has been inappropriate.
There might well be an organisational, income and intelligence and earning potential difference in your households. You have grandparents helping i think - 4 adults in the home helping with the child when with you. The ex is a single working mum. It's hard for her. She needs more support and you being ever present in the new school will make her hate you.
You and DP are saving for a house. Now he is a dad DP needs to forgo more of his income to support his son's house. It's a good idea for you to see this in truth. It WILL impact your financial lives together. As your DP earns more, he should contribute more.
Your intentions are so caring, but the best care you can give is to be supportive of the parents cooperating in their childcare.
Looking at this from the outside, I think it would be charitable to drop the law case, eat humble pie, if there's an income imbalance then making a financial gift and also promising that the birth mother will see you two working at rebuilding trust and cooperation (and perhaps you will fund the 5th birthday in any way she wants, and that the step mother will stay outside of school mother friendships so the birth mum can establish herself there if she wants.)
I'm a step mum and mum. Our kids get a mix of educational support and birthday celebrations in each mums and dads houses, settled amicably between both parents. We uphold the other parent. The birth parents are primary carers, the step parents are supporters.
When my babes were little, starting school, I made really good mum friends and I have kept them, decades on.
The best outcome for you personally is not to WIN over this, it's if you can feel secure in knowing you have done your best. Your best for this child needs a rethink. The best in this case is that the birth parents share the parenting, perhaps you generously give a few more clothes and help the boy with learning the alphabet, you let his mum bond with the child's new school friends families and you retreat a bit, and be less in her face. Make it your policy to say nice things to others about the mum when asked.
Perhaps the root is that the birth mum would have liked a life with the dad. Unlikely tho...she didn't tell him she had his baby, for years. A dodgey mothering tactic on her part, but it is what it is.
Your DP will love you more if you are warmly supportive rather than an agitator. I know you want a good outcome, but fighting makes everyone sad. If you're strong, and a bit detached, the current fight hurts you less. But in the long run it often hurts the partnership with DP.