Could anyone help me figure out how to set up dual monitors with this laptop and docking station?

Hi,

I have a Lenovo Thinkpad T560, and two monitors.

The T560 has no dedicated GPU. An Intel 6600-something with Intel HD 520 Graphics.

I bought this docking station:

https://www.amazon.com/Lenovo-ThinkPad-40A10090US-Docking-Station/dp/B00G6T8EK2/ref=sr_1_10?crid=2ECOVLF3UJGMX&keywords=thinkpad+t560+dock&qid=1666666467&sprefix=%2Caps%2C77&sr=8-10

I connected a DP to HDMI cable from dock to monitor 1. And plugged an HDMI into the laptop's side port to monitor 2. For some reason, this doesn't work for dual monitors. It only shows the DP output on monitor 1 if both are plugged, and the HDMI only works when the DP is unplugged. Windows or Intel HD graphics does not recognize both displays at the same time.

So I found an old DVI to HDMI cable sitting around and plugged that into the dock. DP to HDMI on monitor 1, DVI to HDMI on monitor 2. Both outputs coming straight from the docking station. This doesn't work either, same story as the last.

I was searching around and found another dock:

https://www.amazon.com/gp/product/B07J6B744T/ref=ox_sc_act_title_1?smid=A30JMM27KWLBI2&psc=1

Which has an extra DP and an HDMI port, but I'm hesitant to even buy it for fear of the same situation. I read a few different answers in the Amazon listing for the first dock linked that people have it working with dual monitors. But I have no such experience.

At this point I feel like I'm going through some kind of drawn out bureaucratic process. Nothing I try works. There are two output ports on the back of my dock, why doesn't that make for two outputs? Does anyone have any idea what I can do, short of buying the other dock, and can anyone say for sure that the other dock will definitely work for dual monitors?

Thanks.