To keep the story short here are the ingredients. My wife and I sketched the design first and then looked for the pieces in IKEA.
IKEA items used for the DIY trolley table:
2 x SNUDDA lazy susan
LINNMON table top (100 x 60 cm)
ALGOT shelf (40 x 38 cm)
BOLMEN toilet brush/ holder
LACK side table
EKBY VALTER brackets
BETYDLIG curtain rod holder
We bought 2 of the SNUDDA, painted them with red spray paint (metallic colour) It took almost two cans of spray paint. The SNUDDA is for cake, I guess, but it is solid enough for the wheel.
We bought the LINNMON table top during a sale. At that time we weren’t planning to build the table yet. So this came in handy when we needed it.
For the shelf beneath the table top, we used the ALGOT shelf.
Now, the interesting part :). We used the BOLMEN toilet brush as the connecter to connect the base of the table top to the suspended ALGOT shelf beneath. The one we bought was originally in white. We cut off the brush part and used the rest of it. It is holding the shelf with its grooves.
For the other legs, we used 2 from an older IKEA LACK side table. We painted them white, as the table I had was in brown. Connect the LACK legs to the LINNMON base with brackets.
To connect the table top to the wheel, we used the EKBY VALTER bracket. We bought two of them and painted them the same red. You can find these brackets in the shelves section of IKEA.
Another important thing, to connect the shelf with the wheel we used the BETYDLIG Wall/ceiling bracket for curtain rods. The ones I had were black in color, so painted them in white.