Help me choose a relay to control the solenoid valve in the washing machine

Good evening! Please help with the selection of the (actual) relay. There is a situation: the parents have an automatic machine in their summer cottage, you need to somehow “trick it” so that it works from the “baby” pump. After wandering around the Internet and after a little reflection, I decided to do this:

Make a closable power circuit for the "baby", which will be closed by a relay connected in parallel to the solenoid valve in the washer, which is controlled by the washer programmer. In theory, when the typewriter “needs” water, it will open the valve, applying 220V voltage to it, the valve will open, at the same time turning on the relay, which will close the “baby” circuit and the water will go. When there is enough water, the washer will close the valve and, it turns out, will open the power circuit of the "baby".

Everything is easy and simple, but here is the situation:

a) I’m not good at electrics and (for now) I understand only how an ordinary relay of only this type works (it’s 12 volts, because everything is very clear visually):

b) I have 2 VALVES on the typewriter, which work separately. That is, you can throw 2 relays by connecting them at the output (so that the inclusion of any valve starts the pump, but does not turn on the second valve). Ideally, I would like to find a relay in which there are 4 “inputs” (2 independent 220 each) and 3 standard outputs (main and NO with NC).

By the way, if I'm not mistaken, then I need to connect to NO, so that when voltage is applied, it closes and turns on the baby. That is, it is interesting to know: is there such a relay where you can connect 2 wires from one valve and 2 from the other and the current flow through any of these two pairs closed the baby's power circuit. (as in the 2nd circuit) or what kind of relays are there that are suitable for the 1st circuit?

Thank you so much. I apologize in advance for my "art".