As others have pointed out, you can't really share DBI handles between processes. The easiest thing to do by far would be to spend a few dollars on more RAM for your database server and keep on using lots of connections. However, if you really need to limit your connections you can use DBD::Proxy for this. It's slow, but it works.

Another approach is to use Apache/mod_perl as an application server, putting your core code in there and calling it from clients via SOAP or RPC-XML. This would let you limit the number of connections at any given time by controlling the number of Apache processes, but it also means a significant re-write of your code.