Even if it feels a bit embarrassing, if you only want to pay for what you have had, you simply do have to be clear about it upfront at the start of the meal. It isn't other people's responsibility to mind read and saying it at the start is important, so no-one feel ambushed later.
The problem is the OP felt ambushed by a decision made by one person at the end of the meal. She didn't like it. Equally people, don't like it when someone announces at the end that they want to do the bill in a way which will disadvantage them. Being upfront is so important.
If you have plenty of money or don't care about how the bill is sorted, then You have the luxury of not needing to speak up at the start of the meal. If you really need to only pay for exactly what you have or that's what you want to do, however awkward you feel, then you don't have the luxury of waiting and seeing how it all pans out - because a splitting decision is very very common.
So OP needed to speak up at the start. She didn't and no one else did until the end and when that happens, often whoever speaks first determines how the bill will be paid. It's hard to avoid this - so pre-empting is vital if the outcome really matters.
It's tricky when it's someone's birthday. Social awareness comes into it, so not embarrassing the birthday person. OP could have said at the start, that she was keen to pay for herself, but that would prompt a discussion about paying for grandparents in front of them. Not what you want. She could have said that she's like to pay for herself plus a share of the grandparents too - but then there could be someone (like op) who objected either openly or on MN because they weren't consulted and couldn't afford it.
Perhaps the ideal would have been to text round beforehand and suggest paying for grandparents, plus Op could only pay for her meal and not bill split. It's becoming convoluted and complicated, which is why people often don't do this, but actually do what the aunt did and have one person pay the bill, to remove any awkwardness from the grandparents and sort it out afterwards. Of course the problem was that OP wasn't there later to voice her dissatisfaction with how it was worked out. It's hard to complain if you're not there. It really wasn't the mothers job to say what OP would like to do or for the aunt to predict - the aunt was managing the situation with the GP in mind and looking for a simple solution - seems reasonable in the situation, given OP hadn't expressed any thoughts on the matter at all.
Key point; if you feel strongly about these things and really don't want to split, you must say so in advance. If you don't, it's difficult to moan about it. Your idea of not splitting is no more or less valid than the view that splitting is best.