Whilst in most ways it is much more difficult to be a single parent, this perhaps will help here, as your house, your rules and no one to disrupt that!
If DD is only with exh 2 days a month that will not matter.
I am prone to piling on the weigh fast like DS, DD is naturally v skinny like her father.
So l know how hard it is to always be eating super healthily whilst others have lots of bread and roast potatoes, but having a DS like me, has really motivated me to be aware of getting him to accept through seeing for himself, that once treat times are done, ie parties, Xmas, healthy eating is the norm and can be enjoyable too.
Yesterday DS called out 'just getting a snack before dinner ' he had a huge handful of green beans, raw, in one hand and a chunk of cheese in the other. If there was plenty of chocolate or biscuits in the cupboard l doubt l would be able to keep him at a healthy weight.
You do have to be prepared for the tears and tantrums, as your DD is used to having what she wants with food, but remember it is not making her happy being overweight, ( or healthy) and as soon as she feels better and lighter she will be delighted.
l find if my mind is really made up regarding a difficult issue and l am not prepared to discuss it, because l am sure l am doing my best for them they soon sense my resolve and calm down.
Be prepared to stay calm and not react, shout or justify. Hope it goes well.