Replacement of dimmer switches with Shelly devices

[Coyote]

Hello,

first and foremost, I have to apologize for being an electrical layman (mostly), not knowing the exact details of the issue the electricxian told me about or of the layout of the wiring, and also not knowing the correct technical vocabularies. But I give my best.

When we moved into the house we had bought, we had the electrician re-build the living room lighting's wiring. The setup is like this:
a dimmer switch (Busch-Jaeger 6526U) together with a regular push-button in the dining room, controls a set of LED lights in the ceiling. Since there are two sets of LED lights, the whole setup exists twice, but that shouldn't really matter to the issue. Both dimmer switches and push-buttons are placed immediately next to each other.

The problem is that either the dimmer switch or the push-button (depending which set of lights you pick) won't work properly, in so far as that it's difficult to turn off the lights. Dimming works and switching them on mostly, too, but one has to press the dimmer switch or the push-button respectively sometimes a couple of times until the lights go out again. On the set where the issue is at the dimmer-switch side, the push-button turns off the lights quite reliably. On the set where the issue shows at the push-button, turning the lights off with the dimmer-switch works mostly well.

From what I understood from the electrician (whom I trust and who has proven himself more than once), the house's old and cheap-skate wiring doesn't provide - as far as I understood it - a protective conductor was omitted from the switches in the dining room. The resulting difference in potential - I think - leads to the issues. The electrician tried to solve this with a capacitor. It helped somewhat, but not enough.

So I started wondering whether I could replace the dimmer-switch/push-button "internals" with something smart (I do not want to replace the LED lights, though), so the inadequate push-button wiring isn't needed anymore, but I'm not familiar enough with the Shelly (or other) products to find out how. Would anyone have a suggestion?