I wish my ex behaved like you.
No, she cannot dictate how you spend your money, you share looking after your DS, you work and pay maintenance. Taking him for a meal and buying a couple of magazines is kind of par for the course of being with your son if you have a wee bit of spare cash.
For comparison, my ex is a self emplyed trradesman, he owns a house in his own name, and co-owns a house with his new wife (who works full time). Due to a fuck up with solicitors, which is too complicated to explain, he left me with the full debt of the joint mortgage, walking off with the £35.5k that he should have paid into it, which I think he used as a deposit on the place he now shares with his new wife. He filed that his buisness made a loss in the last tax year (I did his books for the 7 years previous to that and he was never any where near making a loss, and he worked longer hours after he left), but as a result the CSA had no option but to say he should pay £0 maintenance for our 2 daughters, even though he was on holiday in Malta when they phoned to discuss his dispute. He sees the girls every other weekend, and they have regular shopping trips, cinema trips, petting zoo, soft play etc, every time they go to his. He frequently buys them toys, clothes, dvd's, DS games etc, none of which ever come home. He does not contribute to clubs, school unforms or school trips.
I have an older DS too, who is hoping to go to college next year, and I am a full time student, I live very rurally, so to get the kids to school I need to run a car. Last summer I discussed with the kids what we were going to save up for, and the decision was a bicycle carrier for the car, so that we could take all of us and all of the bikes to visit my dad during the summer holiday (my dad is a keen cyclist), I used my birthday money sent to me by my dad to buy it in time. When my ex found out what we were planning to buy, he told me I ought to be prioritising my money on the children.
Personally I don't think you have done anything wrong, you are not spoiling your DS, nor neglecting you financial responsibilities to him. I would buy him ice-cream, and if you can manage it a trip to the cinema would't harm him either.