Changing a tongue jack safely can be a bit of a challenge...first jacking up the tongue with a bottle or other jack and then securing the load on jack stands or other supports.
With that in mind, a working tongue jack allows you to hitch up to your tow vehicle and change the jack with the coupler on the hitch ball.
All that said, it may be worth a bit more effort to free up your current tongue jack to enable an easy, safe swap.
The tongue jack is just a
"lead screw"...threaded rod...that spins in the "nut" attached to the top of the hollow tube that extends or retracts to raise and lower the tongue. (Link is just an illustration.)
The "nut" on the hollow tube is probably rusted/frozen to the lead screw.
How to "fix" that. Drill about three holes into the side of the pipe tower on which the motor sits...and that attaches to the tongue/A-frame with (typically) three bolts. Through these holes, spray a good "
penetrating oil" style lubricant...don't waste your time with WD-40. Spray this on liberally with the goal of getting plenty of penetrating oil on the lead screw where it engages the nut on the lift/lower tube.
It helps to estimate where the nut might be in its travel up and down the lead screw based on how far the tongue jack is extended.
Let it sit for a while...maybe a day. Gently test with a hand wrench. If no movement, apply more and wait another day.
This may or may not free up the nut on the lead screw. Whether or not it's worth the effort depends on the soil conditions and your equipment available for safely jacking and supporting the tongue while you replace the jack, If you have a good jack, jack stands, and blocking to support all that on "soil", just buy a new jack. It only takes removing 3 bolts and one wire. But if your conditions and equipment are sketchy, you might try the penetrating oil so you can change the tongue jack with the hitch on your hitch ball.
BTW, if somehow you actually salvage the tongue jack and keep using it, you can cover the holes in the jack tower with a couple of wraps of electrical tape to keep the crud out.