I have the Trio 7" Dual core tablet. The battery is not charging completely, can this battery be replaced and if so where do I find the battery in the unit?

Battery replacement is possible. The battery is a flat component encased in a shiny silvery sheath behind the speaker area inside the back cover. It's mounted with double-sided (very) sticky-tape. A replacemnent battery should be sourced, having the same power specifications as well as physical dimensions. (see detailed close-up photo attached.) Replacement involves desoldering the 2 terminal wires (1 red and 1 black) which attach it to the main board, and replacing the battery with a new(er) unit.
The above having been said,I'd only replace the tablet battery if I was sure that it's the battery at fault. Here's what I'd suggest.
First, check that you're using a charger with the proper 5 Volt / 2Amp (2000milliamp) output. Also I'd suggest you use a charger designed to be plugged intothe G2 7" Dual-Core tablet's dedicated charging port. (See sample tablet charger in attached photo) The G2 tablets WILL typically accept charging output via the micro USB port, for example, from a typical cell phone charger. However typical phone chargers which will happily attach to the Trio or other similar tablets, via the micro-USB port do NOT often have the same output power specifications. This I think may cause difficulty with the tablet battery not reaching the fully-charged status. Also, the use of the USB port for charging may cause access problems if the battery power is low during some operations (eg data transfer in slave mode), as the charging port can not multitask as the USB port can. If power to the main boad is lost during such operations the tablet may become "bricked". Bottom line for me would be to use the dedicated appropriately rated charger whenever possible: it's the reccommended charging method.