but we have also lost our internet connection for short periods of time so I'm wondering if the power conditioner was having a negative effect on that signal as well.
More than likely, the conditioner allows forward signal , but not reverse, so this would explain why you would lose internet connection.
If that's the case, should I consider going with a three way split
This will make things worse.
What you need to have done is to have a dedicated line installed for either the tv or modem ( doesnt matter which one ) , but it has to be dedicated.