I would give the priest a call rather than approach them after mass. It's a very busy time with everyone wanting to say hello to the priest after mass and he won't be able to give you the attention and may resent having his attention diverted from the regular mass-goers. We rang our priest first (just by luck tbh) and he said he was delighted we called instead of approaching him after mass as people didn't seem to absorb what a busy time it was for him.
I think this totally depends on the individual priest. I used to live in a parish where the priest would not take a phone call, he expected you to approach him after mass, so you therefore had to go to mass! Always best to telephone the parish office and just check the local protocol!
Are you planning to have the wedding in your current parish or the parish that you used to live in?
If it is not your current parish you might be asked to arrange your own priest. But you should be ok in your parents parish.
Best of luck with your planning and welcome to WOL
Our church is in our old university and we have to provide our own priest. I think if we were still attending the university the chaplin would do it but we're long gone. Luckily FH's family are on very good terms with their former parish priest and he is happy to do the mass for us. Otherwise I would have been on to my grand aunt and had her track down a priest for me through her prayer circle!
If the priest knows your family you should be ok. Ask first and pretend you know no different.