Instead of a text description of your system, it would help us if you could draw a sketch showing all the system components. You haven’t mentioned a pump in your description, but I assume that there is one. If you can’t do a computer generated sketch, something on paper that you’ve then photographed would be adequate.
Photos would also help us to understand the different components of the system.
Is the in-floor tubing in concrete or under some other flooring material?
How do you know that you do not have a leak? Have you run a pressure test? In my system I pressure tested the tubing and manifolds at several times operating pressure for a day. When I was satisfied that there were no leaks I put the system into operation.
If the relief valve on the system is set at 20 psi, then your operating pressure should be significantly below that. Is the pressure gauge upstream or downstream of the pump?
A successful hydronic heating system should have no air in the loop. But, water is highly incompressible, so having a closed loop system filled with water means that there is no room for expansion. Just raising the temperature of the water by turning on the heater would cause the water to expand slightly and with no expansion room in the system the pressure would increase dramatically. That’s the reason for the expansion tank that Missouri Bound mentioned. If you don’t have one that could be the cause of the dramatic pressure swings that you’re seeing.
Pressure and temperature gauges are essential for you to know what’s going on with the system. For example, if you’ve put hardwood over hydronic heat the manufacturer will have specified a maximum subfloor temperature when used with hydronic heat.