@jschlapi: How can an Access database be split across two servers? This sounds very suspicious. Also be aware that if you are accessing a remote server (not on your LAN) your problem may be more with networking than with Access per se. Also that would be dangerous because a lost connection could leave your database in a corrupt state. Not good.
As far as Access alternatives, there are numerous choices. Any good server database would be fine. Probably sql server express would work admirably here, as long as the storage limitations aren't a problem. Also Oracle Express, MySQL, MariaDB, sqlite, Firebird, PostGre, and I'm sure others I don't even know about. With the open source DB's you'd need be sure you get an ODBC driver to be able to handle the connections. For SQL server express and oracle express you could use ODBC or use (I think) providers that are created specifically for connections with those types of databases.
@gingertrees: I'd go one further and say all access databases should be split. Although I have rarely found a database to go corrupt (on my one-user databases -- count in 7 years of use is "once"), it is still better to protect your data by putting it in a backend, since if corruption does occur it would mostly like be in a front end object like a form or report. An exception might be if the data can easily be refreshed, or if you are okay with restoring from a backup in the event of a problem (as I often am so I don't actually follow my own advice here). And oh yes, we always have a good back plan, folks, don't we ...?