It would appear that your tractor is a 1990.
I want you to understand that I believe what you are telling me. But I also want you to understand that it makes no sense.
The J-26 three point hitch will fit onto any 4000 Series tractor and work perfectly. The same holds true for the older rear PTO kits. They are just a valve that redirects the flow from the pump to whatever attachment is connected to it. If you reused the steel lines, then it is pretty difficult to connect them incorrectly BUT.... even if you did get it wrong.... that still would not account for what you are telling me.
The Colt/Case and Ingersoll Hydriv system is known as an open-center type. Oil leaves the reservoir and floods the inlet port of the pump where it is pushed to the outlet port. From there, the oil flows directly to ....and through the rear PTO valve before going to the IN port of the Travel/Lift valve and then to the oil cooler before returning to the reservoir for the next trip through the system. As long as the engine is running, the oil is constantly flowing as I described.
But the PTO valve and the Travel/Lift valve are there to cause the oil to take a short detour so that work can be performed. If you move the lever on the right side of the steering wheel, the 3 point hitch will go up or down and so will the mid-lift that the deck/blade/blower is attached to.
If the lever on the left of the steering wheel is moved, then oil will be diverted to the drive motor to make it move the tractor in forward or reverse. Both of those functions have their own separate relief valves built right into the casting, next to their respective spools that are controlled by the hand levers. Think of those relief valves as being the same as a circuit breaker in the electrical system of your home. If what you are doing causes the oil pressure to rise higher than the setting of the relief, then that relief will open up and let the oil bypass right back to the outlet of the valve. You will often hear a squealing sound when that happens.
The rear PTO valves are built the same way. They also have a relief built into them that will open up whenever the oil pressure exceeds their setting. These reliefs are there to protect the pump and other parts of the hydraulic system. The relief in the PTO is usually set to blow off at about 2200 PSI. The relief in the travel valve will open at around 2100 PSI and the relief in the lift valve is set at a mere 575 PSI on the garden tractors. I tell you this so that you have a clear understanding as to how your hydraulic system works.
When no work is being performed, the hydraulic oil freely flows through the system at less than 100 PSI because nothing is impeding it. Pressure begins to rise quickly whenever you move a lever and ask the oil to perform work. The harder the work, the higher the pressure. In other words, it takes more pressure to make your tractor move up a steep hill while pulling a garden cart filled with dirt than it does to pull that cart down your level paved driveway. Pressures in the system will rise and fall constantly in accordance with the difficulty of the work being performed.
In order to isolate this problem, I think that you are going to have to disconnect the lines coming from the PTO valve and hook the pump output line directly to the travel/lift valve just like it was originally. The purpose of this test is to make sure that there is nothing wrong with the travel spool.... internally. If the tractor functions perfectly, then we are left with the PTO valve as being the problem.
I have never heard of a PTO valve giving problems of any kind providing they were properly plumbed into the system. But even when the lines to the IN and OUT ports were reversed, the tractor still functioned perfectly normal. However, with the PTO lines reversed, the relief valve can no longer do its job of protecting the pump. If the rototiller is being used and it strike a big tree root that causes it to stop spinning, then the pressure of the pump will rise higher than what the pump housing can withstand and the housing will sometimes crack open or the front seal of the pump will blow out.
In this instance, you are blowing a hydraulic hose but that hose is subjected to the same pressure no matter which way you move the Travel Lever. So it makes no sense to me that you report being able to back the tractor up with no problems but.... have that hose blow whenever you ask the tractor to move forward. If you are using hydraulic hose that has a WORKING PRESSURE rating of 3000 PSI or higher, then it should not blow open. The pump should fail long before the hose reaches the rupture point because hoses have a safety factor built into them that is much higher than the working pressure rating.
To be honest here, I am grasping at straws with this question but..... did you thoroughly flush out the PTO valve and lines prior to installing that kit on your tractor?