I'm building a website using Rstudio in Rmarkdown.
Are you using R Markdown website ? or another output format like blogdown or distill ?
With default generator for R Markdown all the rmd files are rendered. Unless you have set new_session: TRUE in your _site.yml, they should be rendered in the same environment, so they should share the object created. Take care of the order of rendering in this case. It should be alphabetical.
However, if new_session: TRUE, then a new R session will be used for each Rmd file. In that case you can't share the workspace.
Safest way to share elements would be to use a caching-like mechanism. For example, you can use .Rds format to store your object with saveRDS() in dataCleaning.Rmd to read it later with readRDS() later. See the doc of these functions 2readRDS(). Any other file format would work. The idea is write to disk to read it later.
Know that you can also share common content between files
Hope it helps