Is there a way to combine two signals with a splitter so they *don't* interfere?
I don't know of any way that will guarantee success when you combine two UHF antennas aimed in different directions with a splitter in reverse; you just have to try it because of so many variables. The Antennas Direct DB8e ads imply promise, but ADTech who works for Antennas Direct and gives good advice here, says that it doesn't always work. He says that it is most likely to work if the two directions are 90 degrees apart.
CATV systems use separate antennas, single channel amplifiers, attenuators to balance signal levels, and combine into a single system. That costs thousands of dollars.
Anything you do that costs less, will involve making a compromise.
There are a number of less expensive ways, but they will not give you everything you want unless you reduce your expectations and prioritize.
You can do the project in steps, with the first step the DB4e in different directions to see what is available.
Then you must make a list of the channels most important to you, which will determine the antennas, amplifiers, and directions.
Some people in your situation would use one all channel antenna and a rotator, but rotators have some disadvantages, like do you want to wait for it to swing around to another direction, do want to repair it in the middle of January, and do you want to rescan after changing direction if your TV can't add a channel after scan?
If most of your channels are in one direction, you can add a few from another direction with a custom combiner by Jan Jenca.
You can use an A/B switch to select which antenna to use, but your TV will need to rescan if it can't add a channel after scan like a Sony.
You can connect the main antenna to the antenna input of the TV and connect the second antenna to a separate tuner, with its output going to the aux input of the TV. This my favorite low cost solution.
You can have one antenna going to one TV, and have the second antenna going to another TV.
If you are into computers, you can have a network of SiliconDust HDHR tuners.
Can I combine the antenna signal with my existing in-house cable lines, which also carry my internet? Currently I have Shaw cable internet and TV.....
Not a good idea, because the cable TV signals and the OTA signals use the same frequencies. Also, there is a chance that the antenna system will radiate cable TV signals, some of which are on aircraft control frequencies. In the US, the FCC sets strict limits on radiation from cable TV systems, which is called egress (signal leakage).
However, here in the US, COX cable TV and internet service can share the same coax, so it might
be possible for the same coax to share OTA and internet.