If your Rega doesn't skip in the same location as your Ariston skips, then probably you don't need to replace the house
You might want to look online for instructions on setting up Ariston or Linn suspension; your suspension may be set up to be too bouncy.
I recall in my RD-11 there were little bits of foam between the springs and the positioning bolt that were probably meant to provide a bit of damping. Does your turntable still have these?
Does your Ariston always skip in the same direction (toward the inner or outer part of the record)? May be levelling, azimuth adjustment, antiskating, or arm bearing problem. Try disabling the antiskating first. Check to see if the top of the cartridge is relatively parallel to the record surface left/right and front/back.
Is the cartridge suspension worn out? Watch while playing and see if the cartridge bottoms out or contacts the record when disturbed.
A few ideas anyway.