We are facing same issues.
We had created child tickets using task, there is no such option of linking client of parent ticket to other child tickets as there are other LINK TO PARENT options.
We seek for a support from SolarWinds regarding this and received a response that they will treat this as a feature request.
For the time being we have created a feature request on thwack for inheriting client information from parent ticket to child tickets.
Please follow the link below and thumbs up our idea.