I do not carry a jack for tire changing. I have used my hydraulic leveling jacks to assist with raising front or rear of MH. Plus have a jack stand for protection.
To remove lug nuts I have a 3/4" breaker bar, 30mm socket and 4' pipe that fits over breaker bar. Unlike most C's the lug nut are not torqued at 400 lbs ft. This requires heavier equipment.
I have used road service 2 times in the 10 years I have owned my MH. Both times service people did not have correct equipment to service the MH. I like the idea of having correct equipment to get job done regardless who does the service.