From the description, it sounds like the neutral may be shared between the two circuits, which you can't do with a GFCI. The GFCI is looking for an imbalance of current on the hot and neutral lines, so if the neutral is shared with another circuit, there will be some current returning on the neutral that did not go out on the hot.
If you can trace the circuit and find the connection between the neutrals on the two circuits, and isolate them, that would be the easiest and cheapest fix. If the neutral is shared via a multiwire branch circuit from the breaker and can't be split, you can change the gfci breaker to a standard breaker and install a gfci outlet after the neutral splits for the two branches. And I'm also seeing two pole gfci breakers which would allow you to replace the two breakers with one that provides gfci coverage to both circuits and should handle the shared neutral, which may be a good fall back option if you can't locate the shared neutral.
Uh-oh. Your voltage (hot to neutral) should not be 130V anywhere except a few countries where 127V is common.
Start by measuring across the two hot "legs" in your panel. This value should be 220-240V, tending toward the latter, e.g. 238V.
Now measure each leg to neutral, these should be very close to half that, and very close to each other, e.g. 118-120V.
If they are not, but the two values add up to the first number, you have a very dangerous condition called a "lost neutral": the two "hots" are good, so 240V machines are happy. But the "neutral" is floating, and voltage on each leg is going to vary all over the map as the loads change, e.g. 171V and 67V, which will cause your appliances to catch fire. If you have this, shut off the main breaker now and unplug everything 120V or 120/240 until you fix it for good.
In light of your dryer error, a more likely possibility is that you have lost a leg of "hot". In this case, all the 120V circuits on that leg will be out, while the ones on the other leg work fine. 240V-only appliances will not work. 120/240 appliance controls may work, but the heaters won't. This is not an emergency in the same way as a lost neutral.
You may be having this problem with your entire house, it may have only appeared first at the pool. I gather your dryer is not at poolside.
The answer for any kind of "lost" wire is to give the panel a thorough take-apart and inspection. Look for loose screws (prticularly on heavy-wire lugs), corroded or arced contacts on breakers, burnt busbar, etc.
If you have a smart meter, good chance the power company can turn it off remotely using their SCADA system with a phone call.
White to green: In a properly wired house to code, with the main breaker off, resistance between neutral and ground should be as close to zero as your meter can detect. Voltage should be zero obviously. However, if any circuit is on, all bets are off. Voltage may be somewhat more than zero (but not more than 6 volts), which will make it impossible to measure resistance.
Best Answer
Your devices are NEVER broken
Let's be clear about this. GFCI is a fault-detection device. It detects ground faults, mainly in appliances, but it can happen in wiring too. However, ground faults in appliances only happen to other people. YOUR appliances never ground-fault!
So definitely leave everything in the garage plugged in, and don't go unplugging anything to troubleshoot.
Narrow it down
What's left? It could be a hardwired appliance like a lamp, but it would have to go to a neighbor's house, because your lamps don't fail!
It could also be a fault in the wiring.
A hot-ground hard fault would trip a regular breaker. A soft fault (leakage) might not, but would surely trip a GFCI. This might happen if a box was getting wet, or if outdoor wiring was leaking (perhaps because it is not rated for outdoor use, e.g. NM "Romex" outside or buried).
A neutral-ground fault will not trip a breaker, but will trip a GFCI. This could be a bootlegged ground, or a neutral screw touching a ground wire at a receptacle.
Look at the cable to the garage. Is it /3 cable with a black, red and white wire? That's the problem right there: This type of wiring* is incompatible with single-pole GFCI breakers. First, the black and red wires need to be on a 2-pole breaker with common shutoff, regardless, for safety - they must shut off together. Then, you need to use a 2-pole GFCI breaker, because it need to measure all 3 wires - both hots and the neutral.
Another potential problem is if two separate circuits (not MWBCs) unintentionally mix their neutral wires. That's a perception problem among installers: you should intermix all grounds from multiple circuits, and some people think they should intermix neutrals too. Or they need a neutral wire, so they grab one from another circuit. That's very common with smart switches and in boxes with 3-ways. (Thanks DoxyLover).
All these problems should be observable by opening up the junction boxes (with power off and tested to confirm off, obviously).
* It's called a Multi-wire branch circuit and there's nothing wrong with it, however it does require knowledge and special handling, GFCIs being one such case.