Hi sdvh,
Your heating and cooling system has multiple thermostats; one for each air conditioning unit. Only one of those will operate the furnace. I'm not sure which, but you should try all three. When the thermostat calls for heat, the furnace blower should start and run for about 25 seconds, after which there should be an ignition attempt. The ignition will try 3 times and if no flame is sensed, it will lock out for safety. The thermostat has to be cycled out of furnace/heat mode to clear the lockout.
One common issue is how the propane tank valves are opened. If opened too fast, a safety overflow protection device activates. Close the valve. Wait 15 seconds. Re-open the valve verrrrrry slowly.
Make sure nothing is blocking the air return or any of the floor vents. You must have good airflow for the blower to get up to normal operating output. If not, the blower will run for 25 seconds, but the igniter will not fire.
Check the vents outside to make sure you don't have debris or insects.
On the water leak, you must investigate this and find the issue. Water leaks that are allowed to continue can cause serious damage. While the warranty will cover fixing the original defect, if you allow it to continue, you may have to pay for repairs needed to fix the water damage.
You may just have a loose fitting that needs to be tightened a little. Most of the plumbing is behind the Universal Docking Center (UDC) and can be accessed by taking down the rear wall of the pass through basement storage.
As for mobile service, you might check with your campground manager, or call nearby campgrounds. They usually know about mobile servicers. I see there are some listed by Google Maps within 100 miles, so you might incur a steep travel charge, but the alternative of hauling your rig to a service location could be even more expensive. If you find one willing to come out, get prior approval from Heartland for warranty reimbursement.