mm I have nothing further to add except just to say that I still wish my parents had broken up. Lving with parents who tolerated each other then as time went on actively hated each other meant that I was out of there as soon as my A Levels were over and rushed into some really damaging relationships with some really nasty pieces of work. Each trip home was blighted by the underlying atmosphere of resentment.
When DD1 was a few months old I went back home for the first time since my dad died and it is pretty much the only happy memory I have of that house. The first time we all got on, and I wonder now that, if they had broken up, I wouldn't have had so more happy memories and been more self confident and happier in my own skin as I grew up.
My mum spent 40 years in a loveless marriage and I wish she had had the strength to leave and find happiness. I'm not comparing your DP to my dad but if you can't work through your problems, and you might be able to, but if you can't there is no shame in walking away. In fact it is a brave thing to do, and as your DP is a good dad then Tilly will be able to spend time with him in a happy home, and with you in a happy home. Trust me that growing up in an unhappy home is hell.