First, the shower presumably wasn't your sister's doing. People don't throw themselves bridal showers. The late invite thus has nothing to do with her.
Second - she called to tell you she was inviting you and wanted you there. She sent you a wedding invitation (which, yes, would be formal if she's sending out wedding invitations, everyone gets the same one) - she's extending an olive branch, as noted by a poster above.
She does NOT mean you to work on the relationship at the wedding. Inviting you to the wedding and calling personally to tell you she wants you there IS working on the relationship.
You go, you're a nice guest, you chat with her about how nice her new husband seems and how lovely she looks and how, after things calm down, you'd like to get together for coffee. Then you go home.
You, of course, bring a very nice gift. It's your sister's wedding.
A gift you gave her five years ago has nothing to do with anything. That sounds like it was a housewarming gift, but regardless, it wasn't a wedding present as she wasn't having a wedding. It was a nice present I'm sure but has nothing to do with this affair five years later.
If you want nothing to do with anyone in your family ever, over a remark your mother made years ago, fine, don't go - it seems that's what you keep trying to justify. However, own it.
Your sister is trying to make peace. If you don't want to, send your regrets.
If you do, you go to the wedding like any other guest, with a nice gift, and then later keep working on the relationship she's trying to save by inviting you.
Second - she called to tell you she was inviting you and wanted you there. She sent you a wedding invitation (which, yes, would be formal if she's sending out wedding invitations, everyone gets the same one) - she's extending an olive branch, as noted by a poster above.
She does NOT mean you to work on the relationship at the wedding. Inviting you to the wedding and calling personally to tell you she wants you there IS working on the relationship.
You go, you're a nice guest, you chat with her about how nice her new husband seems and how lovely she looks and how, after things calm down, you'd like to get together for coffee. Then you go home.
You, of course, bring a very nice gift. It's your sister's wedding.
A gift you gave her five years ago has nothing to do with anything. That sounds like it was a housewarming gift, but regardless, it wasn't a wedding present as she wasn't having a wedding. It was a nice present I'm sure but has nothing to do with this affair five years later.
If you want nothing to do with anyone in your family ever, over a remark your mother made years ago, fine, don't go - it seems that's what you keep trying to justify. However, own it.
Your sister is trying to make peace. If you don't want to, send your regrets.
If you do, you go to the wedding like any other guest, with a nice gift, and then later keep working on the relationship she's trying to save by inviting you.