I invited my parents round and we had a dinner part
文脈が分かりませんが to invite my parents to a dinner party もしくは I invited my parents round (to my house) and we had a dinner party はいかがでしょうか。
to invite my parents to a dinner party - 両親を食事会/会食に誘う・招く
I invited my parents to a dinner party - (私は)両親を食事会/会食に誘いました・招きました
I invited my parents round and we had a dinner part - 両親を家に誘って・家に招いて、会食をしました
Party with my parents invitedは不自然です。