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I'd like to make a digger or a dumper truck in Kerbal Space Program using the breaking ground robotics parts. I can, of course just use powered hinges, which works, but isn't how tall diggers and dumper trucks work. I want to use a passive hinge and a linear actuator to power it, but this requires making a closed triangle, with passive hinges on all 3 corners. Is there a way to connect a part to existing structure at both ends?

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Yes, there is a part in KSP that lets you connect other parts in a closed loop directly in the SPH / VAB: the EAS-4 Strut Connector.

Here's a quick example of a simple crane powered by a linear piston actuator, with the struts that close the triangle highlighted by the red circle:

Screenshot

The three hinges at the corners of the triangle are unpowered, and were adjusted to approximately close the triangle before their power was turned off. Two sides of the triangle are made out of I-beams, while the third side contains the piston. The hinge at the top of the piston is attached to a small "cubic octagonal strut", which is attached to the I-beam that acts as the lifting arm using the EAS-4 strut connectors.

(It would probably be possible to connect the lifting arm directly to the hinge with the strut connectors, but then you'd have to be careful to make sure the connectors attach to the right part of the hinge and there might be some glitches. Putting the cubic octagonal strut in between makes the attachment easier. I generally try to avoid attaching strut connectors directly to non-rigid parts just out of caution.)

I've tested this crane, and it indeed works:

Screenshot

Here's the .craft file, if you'd like to test and examine it yourself.

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I don't know if you can do this in the VAB, but in game if you're careful, you can connect multiple docking ports between the same two vessels. If both sets of ports come together within some small time frame, they will both dock. Most people use this for huge ships in space that would flex and wobble when under thrust, but it might be helpful for your project as well.

This video should demonstrate the idea fairly well.

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