It will be easier to us when you show what you really have, photos, schematics, links to modules and so on. You are looking at something, and we have to guess what you have.
Do you have the SS pin of the DLHR sensor set high ? So it does not accidentally go into SPI mode.
The I2C multiplexer needs pullup resistors between the Arduino and the I2C multiplexer and also on every (sub) I2C bus.
The Arduino Uno has very weak internal pullup resistors, that might not be enough. The I2C multiplexer module has probably 10k pullup resistors on the Arduino side, but they can sometimes be enabled or disabled and they connect to 3.3V. I suggest to disable those and add 10k external pullup to 5V for the Arduino side.
The MPU-6050 module probably has pullup resistors.
If you tried with 10k pullup, then it should work. You need those anyway, so please keep them to pullup the (sub) I2C bus.