A mod can not help you with any game mechanic, like how resupply ships work.
I doubt anything has changed or a while, so I think you are off in some complaints on them. My main experience with them is in older versions, though.
You should be able to deploy at any planet if necessary. I have however never really had issues with finding somewhere to deploy them. On the "two fuel" problem, I will prefer to deploy at "one fuel" sources, but two is really not a big problem. When I build them or are at peace, I will usually try to find a decent percentage "one fuel" spot for them to sit at, though.
It should make sure to balance the fuel it carries. I have seen resupply ships stuffed with caslon manage to switch to a 50/50 caslon/hydrogen mix just fine.
I have never had an issue with deploying multiple resupply ships at the same source. Two in the same gas cloud, no issue for sure, but gas clouds are a bit more flexible in that in general. A resupply ship and a gas mine at the same planet should not be a problem either. I think I saw a deployed pirate resupply ship deployed under a pirate spaceport of another faction just yesterday, but I do not know for sure that it was deployed. That was on a gas giant.
"Bigger fleets?" Do you run fleets of 300 escorts or something? :) Two resupply ships may indeed be necessary if I run multiple big fleets that see a lot of action and all depend on the resupply ships. There should very rarely be a shortage of fuel sources in an area where many fleets operate. Big fleets may fool the resupply ship into thinking that it lacks enough fuel, so the fleet wants to head way back. Target the resupply ship specifically if this happens, as it will mine more fuel before they arrive, and fleets almost always reserve more fuel than they will require on a refuel order, giving more fuel available than what the game thinks. Never mind that it may be quicker to wait at the resupply ship for it to mine fuel, than to go a long way to find some.
Example. A ship with 1000 fuel capacity has 500 fuel and refuels. It reserves 1000 fuel because that is its fuel capacity, but will only refill 500 fuel. There is 500 free fuel that appears "taken" until this ship is done refueling. If two fleets are to refuel at the same resupply ship (or at any other refueling spot), this "extra fuel reserved" can be a significant amount. A "second fleet" arriving in such a scenario won't find fuel until the first fleet is done refueling, though.