Electronic – How to communicate with 2 devices with 1 UART MCU in AVR

Your problem is likely in using the wrong baudrate: 112500 is most likely a mistake, the standard rate in that range is 115200 (a search of the manufacturer's website for this number finds many hits, but none for 112500). You could also not be producing the programmed baud rate on one end or the other due to divider granularity; sometimes changing the oversampling of the UART can help. EDIT: Specifically, a value of 8 (divisor of 9) will get you 111111 baud from 8MHz if you set the "double speed" mode bit.

Secondarily, you have a problem such as lack of a common ground between the boards, or haven't grounded the scope to them, thus resulting in the distorted waveform. It's not clear yet if that is what the receiver sees, or if it's merely a measurement mistake in applying the scope.

Additionally, have you verified that the un-named external board also runs without a serial level translator? Most modular inter-board serial communications is at RS232 levels and logically inverted from the logic-level signals, though there are exceptions.

I can't answer as to the maximum length, but at 9600 baud I wouldn't expect problems at a metre or two, let alone 10cm. Just ensure there is a good ground wire connecting the two boards.

And that assumes it's permanently wired, and working in a typical lab environment, or your home, rather than in the engine compartment, or in orbit or on a mountain top.

Even in the lab, if you plan to unplug and reconnect it regularly, add that info to the question and someone will advise on suitable ESD protection.