DBCC on SSAS Cube fails

Oh my dear..

First of all. In your case I would like to suggest you to choose the "Process Default" option. If you are using Process Full always you are dropping all data and objects and recreating all of your stuff. You don't need them. Very often the proposal option is to use ProcessData followed by ProcessIndex.

I didn't proces the cube from within the SSIS, but probably SSIS is checking something and locking something on the database. The best option is to use XMLA. If you want to process your cube from within the SSIS you can write a script task to perform the processing - you can find a scripts on the net.

You need to also check if you have a clean data. Check twice in your project and in your data if you have all the keys and so on. If you are processing separately dimension the data is not comparing between measures and dimensions. I am pretty sure that you have some keys in fact tables that have no corresponding values in your dimension. Make an order with this. If you have no values in dimension and it's correct (doesn't exist in the source tables) you can add to each dimension one extra value with i.e. key "-1" and all values like "N/A" (not applicable) and point the not founded values to this record in the dimensions.

And at the end. If you have a big SSAS database please think about a partitioning.

It's a lot to talk about. If you have some specific questions feel free to ask.

Parent-child relationship in SSAS isn't straight forward as we might wish. From my experience in SSAS 2008 linking them both together wasn't simple at all. In those type of cases the most recommended solution would be to flatten the relationship with a (SQL) view in which you link the parent to the child with the date attribute. That view becomes your dimension and on which you check the changes over time. you can find more data about this in here:
http://www.kimballgroup.com/2007/10/design-tip-95-patterns-to-avoid-when-modeling-headerline-item-transactions/
and here:
http://www.kimballgroup.com/2012/05/design-tip-145-time-stamping-accumulating-snapshot-fact-tables/
Alternatively: If you need both the Parent id and the Child in the fact table (because you need to query on both) then in that case I would go on a different direction and include both id's in my fact table. This way you can monitor changes across time as you would for any other dimension.