He went off with a teenager - ouch! What an immature thing for him to do. Good for you for rising above that and getting on with the job off looking after your DD.
Your dilemma are definitely tough ones - what to do about presents once you have split up, how to support contact with an ex who is obviously been giving you a hard time and how to encourage a good relationship with your DP. I can relate to all these issues currently and mt ex is a bum-hole too
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The present thing is always awkward I find. My ex stopped buying me mother's day pressies/christmas etc. on my DS behalf too. At first I rose above it and thought presents were for my son's benefit. But now I give my DS minimal money - and ask him to make the best use of it/make something to give with it. This seems to me a fair compromise and fits with our family budget. He enjoys giving something he has made from scratch.
If you specified that 35 euros was the sum total of the money your DD would get and that presents were to come out of that - then fair enough. Sometimes kids buy because they they believe gifts will bring them closer with their absent parent (buy the way into their hearts) - particularly if there is some animosity between them and Mum. It must be very difficult for your DD to get her head around her Dad having a separate family and making them his first priority. As a mum; that would also cause a lot of hurt when thinking of your DD and sons. It's not an easy one to navigate if she wants to buy for that reason - particularly if you are trying not to display animosity towards Dad and new partner.
From your excerpt; I would be surprised if your DD does not feel animosity - even though it is not overtly explained. I am not sure if this is the same in your case, but sometimes they start to manipulate as a way of gaining control back. They may also see the absent parent as 'golden' (which is easy if they regularly don't do the everyday stuff/discipling etc). Some kids are particularly 'off' with step-parents if there previous family life was shaken and there is residual anger. It is very unfair on your partner, particularly if he has worked hard to provide a stable environment for your DD.
Why are currently buying presents for all your ex's kids? I understand the father's day thing as he is directly related to your DD. But his kids? Do you have a close relationship with them?
As far as the 'no intention of buying for the person who went off with my husband'. I am sure that most women would feel that in your situation. And it is only human to slip up with what you say from time to time. A chat with your DD to explain why you said that at that time may sort it out.
Good Luck