I've RTFT and all your updates OP.
Your DP was not being unreasonable.
The issue isn't bf'ing at 2 which is absolutely fine & normal, nor is it that she has a b/f at night, also normal!
However, breastfeeding to sleep isn't great, as she should be self-settling at 2 - so a b/f, stories, a cuddle & then she goes to sleep. If she's not ready for sleep, there can be a few options for her eg looking at her books, or staying in her room, awake, but expecting 2 adults to be running around trying multiple strategies to settle her is silly.
It sounds like most of the time bedtime works tho. Plus DP is actively involved in bedtime.
Therefore I don't think there's much you need to do.
In terms of last night, I'd have let DP head down, and told DD, it's bedtime, time to sleep, and left her. Just put her back quietly if she gets up, but no chat or discussion. Both you & DP should do this.