How to handle conflict with parents when planning a wedding?
Your question inherently points to some power differences too, you mention the recent clash between you and your mother which also has obviously affected you and your thoughts about this process. I would wonder is there an opportunity to have a conversation with your parents and fiance present, at which time you set forth some group ground rules, like no yelling, one person talks, no judgement etc and each of you discuss your emotional state with the current process (when you do ___, it makes me feel ___) but also come up with expectations that each of you have for things like guest list additions, inclusions, max size of guests. I think there is an opportunity to turn this into a positive experience for all of you, it just seems to not be heading there yet.
Family dynamics, much like anything else depend on clear communication but also that the receiver of that communication also listens without responding- I know that is not always easy to put into practice. I think that your parents are coming from a point of want to provide you with this, wedding as they have it laid out in their minds, its not that they are forgetting or overlooking you but rather feeling their way of going about means more since they are paying for it, hence the power struggle. I think this is common and can recall situations in my own life where this was occurring.
With the idea of give and take there is also the idea of compromise and it seems that in some of the disputed areas neither party is willing to give- and that is ok. I do think that in defining your expectations and your mother's and your father's and your fiance's there will be some areas that each of you can't budge on, but each of you could also look at an area that is less important for you allowing a compromise on some things. This is not easy and as you begin your own family with your new spouse to be, pulling away from your parents there will be more of this like deciding on holidays to be together, rearing of children or shopping for homes, etc... if you can establish a way to communicate with clear expectations on this front I think it would benefit all involved. Be well!