The "Mother" and "Father" bit was a reference to "Effective Medicine for the Worrisome You" https://e-hentai.org/g/539095/e96059d877/ The "flowery panel" joke is also referencing that.
As for the giant gun... I don't know, maybe Patchouli really liked that one guy from S-cry-ed What I do know is that I enjoy reading Satou Kibi's Alice+Patch too much.