Is a drain snake the right tool to clean a long-term clogged bath pipe?
A. Chemical drain cleaner ought to do a reasonable job in this situation
B. Yes there are snakes with attachments like you suggest
C. If you are renting perhaps the inaccessible part of the plumbing is the owner's responsibility.  Without getting into a big discussion about legalities wherever you are, you could ask nicely.
D. Usually a frequently blocking bath drain is caused by someone with long hair who uses too much conditioner.  Get a good hair screen for your tub drain and instruct any such user to clean it during and after each use and to go easier on Hair products.  Require each such user to participate in the disgusting business of clearing the drain.
E.  A common horizontal pipe shared with the kitchen is a whole other level of problems.  I've never seen that before.  The combination of cooking fats etc plus hair is formidable.  Assuming you don't own this mess and can't improve it, you may want to create some kind of Easy Access to do cle an outs.