What rules? Can you cite that?
As an example, the Redbrand hideout in Lost Mine of Phandelver has 1151gp of loot in it, NOT counting magic items. Additionally it has probably around 5 potions of healing in that hideout alone.
You are typically doing that hideout at level 2.
Most encounters will be with individuals, not hordes(entire tribes of creatures or single very powerful creatures that like to hoard like dragons). Especially at low levels like level 2.
It takes 600xp to go from level 2 to 3. A single moderate encounter will be 1/6th of that amount in experience. A deadly encounter 1/3 of it. You're looking at 3-6 encounters to level up from 2 to 3.
The average individual treasure amount for CR 0-4 creatures is 14 silver to 10 gold. Let's say half of them have the 14 silver and the other half have 10gp. Converting the gold to silver and using 6(though encounters will often have less) creatures per encounter, that makes 42gp 6sp per encounter. Totaling that you end up with 127gp 8sp TOTAL for 3 encounters up to 256gp 4sp for 6 encounters.
If you're getting 350gp(including the potion values listed) per person, you are getting waaaaaay more than the book indicates. That number you listed is 4x more at the maximum number of encounters than you should expect at level 2. 8x more at the minimum number of encounters.
And you are assuming that the DM is going to overturn RAW and have magic marts for you to buy unlimited potions at. Even for common items like a potion of healing, the 5e DMG says this...
"Common items, such as a potion of healing, can be procured from an alchemist, herbalist, or spellcaster.
Doing so is rarely as simple as walking into a shop and selecting an item from a shelf. The seller might ask for a service, rather than coin."
Your personal game is atypical of how games are run in my experience. It's pretty Monty Haul with regard to your magic items and money. That's fine as you guys from all you've said here are having a blast, but it's not how the game is run if you are sticking to the rules.
5.5e of course may(and probably did) change those rules, so I'm not sure how accurate what I just said about the numbers is if you are playing 5.5e.