Working on weekends

I have a part time job so I usually work Saturday and Sunday, or do all my hours in one day. It’s the summer holidays now so obviously I can pick up shifts during the week and sometimes have a day off on the weekend. However my problem is that my parents are complaining I don’t spend enough time with them and they want to do things during the weekend. They want me to drop a shift every once in a while which is reasonable enough I guess - but all I’m thinking is the fact I’ve been hired as a part time employee for the weekends. I feel like I shouldn’t be dropping shifts if they’re what I’ve been hired to do - it completely goes against why they hired me. They might as well have just hired someone else if I’m going to be that unreliable. We have a holiday coming up at the end of the summer which I’ll take holiday for and one in the autumn which I’ll take off as well, so I don’t particularly want to be taking all of my holiday and then have none left. Obviously I can take more shifts during the summer holiday but I also feel like these weekdays aren’t even in my contract so it doesn’t matter whether I do them or not because at the end of the day I do a Sat/Sun, these are just extra. Sometimes my rota only has one day during the weekend but then it’d be harder to plan something because I find out a week before.

Anyways, does anyone have any advice? I want to spend time with my family and not be a doormat and miss out on family time just to go to work, but also I don’t want to seem unreliable.

The best solution would seem to be spontaneity. If your know your rota gives you a free day a week in advance then use that week to decide, between you and your family, how you're going to spend that day with them. Not everything needs to be planned weeks in advance.
Also, have you spoken to your employer about perhaps swapping some weekend hours for hours during the week instead? I realise that you were hired for weekend shifts, but it might be that it won't bother them at all if you swap your hours. They may be someone else who would rather swap their hours in the other direction but can't because you're always working the weekends. A casual enquiry is all it needs.