I have been with my DP a few years and he has 2DDs from a previous relationship. There is a 50/50 agreement, so I have a lot of contact with them and quite hands on. The relationship with his ex is strained at times but largely amicable in a kind of 'go along with anything she says and wants to keep the peace' and this generally works out. I help out my DP and at times his ex with school runs, childcare etc when I can so I undertake some parenting roles. However, I do not at any point refer to myself as a step parent, the kids call me my name, and even though we are getting married next year, I won't be taking my DP's last name, as the kids have it too which mean in terms of surname I would share their name whilst their mother doesn't, which I don't think is very nice, I have a daughter from a previous relationship and I don't think I'd like that. So generally I guess I try to be respectful of their mother and how she might feel having someone else involved with her children and to be mindful of this where possible.
DP's ex has recently met someone herself, dating approx. 6 months, none of our business I know but we live in a small town, you fart and everyone knows about it so we know without being nosey. We aren't friends or follow her on social media for obvious reasons however we have mutual friends with her and these friends have approached us to show us what is going on. Both she and the new bf are referring to him as stepdad and even Dad in posts, he is posting pics of himself and the kids online and its all just generally really full on and in my opinion inappropriate and disrespectful to their real and very hands-on Dad. I would not dream of doing half the things they have for fear of upsetting their mother even now after being with DP for years. I told DP I think something needs to be said, because if that is how it is on social media then what is it like behind closed doors, and DP is very afraid that she will be 'phasing' him out of the children's lives by behaving like this. But he is also frightened of bringing it up with her and causing any grief for fear of making things worse.
Also, to be clear this is not a jealousy thing, he appears to be a nice chap who is good with the children and they like him too which is fantastic it just the behaviour is very inappropriate but we don't know how to approach it, it will no doubt get viewed as jealousy. It has really upset DP and caused him to worry that what is currently a very good access arrangement with his children will sour now that another man is on the scene.