There was a thread similar to this recently but as my situation is a little different and I'm after advice more specific to it I thought I would make my own thread rather than take over the other. This could be quite long...

DD currently refers to DP by his first name (she actually calls me by mine too because she cannot say Mum and somewhere along the way learnt to say 'Jess' but will acknowledge me as Mum should others use that term so knows I am Mum type thing). DP has been in her life for a year, we got together around 9months ago. He definitely is a parent to her although we have only lived together as a family for 4 months but he changes nappies, settles her, plays with her and she is a big fan of him (I'm usually the odd one out). DD's Dad is very involved in her life and important to her too, she stays with him for a night every week and also sees him occasionally through the week depending on his work schedule; he calls her, makes an effort to be aware of things going on in her life (comes to speech therapy if possible or at least calls to find out what is new etc things like that), always pays his child support on time and we all get along (including DP and DD's Dad). He is her 'Dad' in everyway possible post a seperation.

DD's Dad and I have discussed how we would handle DD refering to other significant people in her life by 'Mum' or 'Dad' and we are both happy to be guided by DD. There isn't anyone in DD's Dad's life at this point. DD's Dad has said he would be okay for DD to call DP 'Dad' if she chooses although I'm sure he would be a little upset (not sure if that is the right word but you know what I mean) by it, just as I would if things were reversed but I too would accept my DD's decision about what labels to use for those important to her. At this age (2.5) I don't think DD is really in a place to use the term on her own so we don't really expect it to happen just yet (nor do we really have any expectations about it) BUT we are expecting DD's little sister in January which complicates things. DP has suggested we just continue to use his first name for the new baby and DD as we definitely don't want DD to feel as though she has a different or less important relationship with him and we are concerned about influencing her into using 'Dad' for him before she is ready but that feels a bit wrong to me. We have thought about using 'Dad C' or something, more to distinguish between 'Dad' and 'Dad' but feel a bit odd about the fact we are the ones initiating the name change for DD although I'm sure she does feel the parent-child connection with him. She does have a pretty good comprehension so we have thought about trying to explain it all to her -- Mummy and Daddy made her but going on to detail what being a Dad and/or Mum means beyond that and whether she thinks DP is like that to her but it still feels as though we are the ones pushing it. The other thing is that it has only been 4 months living here (although DD was ~18months when DP started being 'around' so a lot of her life has included him) and if it weren't for the baby, we wouldn't even be thinking about this yet which has us reluctant. We also wouldn't have rushed moving in together so soon had we not found out we were pregnant so we are already feeling like we have sped everything up although so far DD seems untraumatized by our lack of planning and we hope she enjoys having a little sister close in age at the end of it all... I love my little family even if it didn't quite happen how we thought, DP feels the same and we can't really imagine things any other way now.

Basically, none of us (DP, DD's Dad and I) are really fussed what she calls who, in the end it is just labels and the importance of people in her life is shown by actions already but I don't want DD to feel as though this new baby is more 'special' or 'important' because DP is 'Dad' if that makes sense? DP feels the same, DD's Dad understands the complexity but really, none of us have any idea the best way to navigate this.

Should we stick with DP as first name even for the baby? Would this even work with other people in our lives probably using the 'Dad' word at some stage in reference to the baby? My Dad actually already mentioned once to DD that she is lucky to have two Dad's who care about her so much.
Do we start talking about using 'Dad' for DP with her? Do we distinguish with 'Dad DP' and 'Dad Dad'? We also thought about using 'Step-Dad' but that obviously doesn't really work with the baby?
Are there any good books around for explaining what a 'Dad' means so we can possibly at least somewhat let DD decide?
Could we come up with something completely unique ('Poppa' etc are out as my Dad is already referred to as such and she sees him at least weekly too so that would be confusing) for both DD and baby to use? Any ideas of what? Remembering it needs to be yellable across a park haha!
How much do you explain to a 2.5yr old? Is it time to have a more formal/proper talk about how Daddy and Mummy made her and DP chose to be part of her life? DD's Dad and I have not been together since she was ~9months so she has never really 'known' us as such.
Any advice, tips, experiences, opinions...