[@The Harbinger of Ferocity] You don't have to/get to roll twice to knock people prone, if you are using the shove action as discussed on PHB p.195-196 under "Shoving a creature". If your first roll succeeds you can just declare that they fall prone (or alternatively push them for five feet). Doesn't seem like you could combine the effects in RAW form, so it's up to the DM to call on that... Sorry about "rules lawyering", I guess I am just too used to doing it. The shove action replaces (up to?) one attack action, so doing both would kinda give you an extra attack.

[@darkandstar] Would the pickaxes be improvised weapons or something else? War Picks are a thing that exist but these are for mining, not going to war so it probably won't count as that, correct?