An Issue here might be that most Animal Companions stack with Animal Companions from other classes.
What might work instead is going Vermin Druid//PF Summoner and have the Eidolon take the shape of a spider, maybe going with the Broodmaster Archetype to have multiple Eidolons.
Perhaps as one of the sides of your 6th level you go Beast Heart Adept and choose a Ankheg, reflavoring it as some kind of burrowing spider.
Then you use the Alternative Summon Monster List variant rules from Unearthed Arcana and theme your Summon lists around spiders of various kinds.
End up with something like this:
Summoner 6 // Vermin Druid 5/Beast Heart Adept 1
Surely your DM would accept this. I should know, I am your DM.
BTW, we need exlpoding spiders.