Welcome!!!
Makes and models would help.
IF you are talking about a Winegard batwing style antenna, it has an amplifier within the antenna itself and requires 12V supplied by the small power supply usually mounted on the wall or ceiling of the trailer/motor home, it has an Off-On switch and often a small light. It has to be turned ON to use the antenna, with the antenna turned toward the signal source for better reception. The amplifier is turned OFF to used a park cable connection in most cases. Check all connections, and check for the 12V on the coax to the antenna and reconnect everything after cleaning.
We have no info for the proposed additional antenna so any comments on it are not possible.
Note that most (but not all) OTA (over the air) signals are now digital and if your TV does not have a tuner capable of converting a digital signal, then you will require a digital-analog signal converter in series with the antenna feed in order to see all the available channels. With a converter in place, the TV is then set to channel 3 or 4 and the channel selection is made by the converter by using a remote control that comes with the converter itself. There is also a small antenna made specially for the Winegard Batwing and mounts directly under it. It improves the reception of digital signals greatly as most are now in a higher frequency range than the original batwing was designed for.
You can connect the new one to the satellite cable, provided it is not being used for a satellite operation. It is only a coax cable after all. But will it work better? Who knows as we have no information on it, it may require a power supply or it may not!! You may require a digital converter or not!! Older TV's with the big picture tube will require a converter for sure. The original bat wing was one of the best antennas available.
More than you wanted to know but... HTH