I think the error was as follows:
1) Data source type "local-tx-datasource" does not support multiple data sources (sqlite and postgresql concurrent transactions). The solution here is to change the type of data source from "local-tx-datasource" to "xa-datasource"
2) Also sqlite does not support "xa-datasource" type (specifically the problem with sqlite was that I could not find an sqlite implementation of the class "rg.postgresql.xa.PGXADataSource", (*) maybe you can find one for mysql :) ), so I change the second data source database from sqlite to postgresql.
This is my "old" data source file:
<datasources>
<!-- Postgresql -->
<local-tx-datasource>
<jndi-name>Postgres1DS</jndi-name>
<connection-url>jdbc:postgresql://localhost:5432/db0</connection-url>
<driver-class>org.postgresql.Driver</driver-class>
<user-name>user1</user-name>
<password>u1pass</password>
</local-tx-datasource>
<!-- SQLite -->
<local-tx-datasource>
<jndi-name>Sqlite1DS</jndi-name>
<connection-url>jdbc:sqlite:${jboss.server.data.dir}${/}db1.db</connection-url>
<driver-class>org.sqlite.JDBC</driver-class>
<user-name>user1</user-name>
<password>u1pass</password>
<connection-property name="autoReconnect">true</connection-property>
</local-tx-datasource>
</datasources>
And this is the "new one":
<datasources>
<!-- Postgresql -->
<xa-datasource>
<jndi-name>Postgres1DS</jndi-name>
<xa-datasource-class>org.postgresql.xa.PGXADataSource</xa-datasource-class>
<xa-datasource-property name="ServerName">localhost</xa-datasource-property>
<xa-datasource-property name="PortNumber">5432</xa-datasource-property>
<xa-datasource-property name="DatabaseName">db0</xa-datasource-property>
<xa-datasource-property name="User">user1</xa-datasource-property>
<xa-datasource-property name="Password">u1pass</xa-datasource-property>
<track-connection-by-tx></track-connection-by-tx>
</xa-datasource>
<!-- Postgresql -->
<xa-datasource>
<jndi-name>Postgres2DS</jndi-name>
<xa-datasource-class>org.postgresql.xa.PGXADataSource</xa-datasource-class>
<xa-datasource-property name="ServerName">localhost</xa-datasource-property>
<xa-datasource-property name="PortNumber">5432</xa-datasource-property>
<xa-datasource-property name="DatabaseName">db1</xa-datasource-property>
<xa-datasource-property name="User">user1</xa-datasource-property>
<xa-datasource-property name="Password">u1pass</xa-datasource-property>
<track-connection-by-tx></track-connection-by-tx>
</xa-datasource>
So.. what I suggest you is to change the type of your data sources from "local-tx-datasource" to "xa-datasource", as I say (*).. you must to find a mysql implementation of the class "xa-datasource-class",
and finally if you can not found this class, you should change the mysql database to postgresql.
I hope I have been clear enough, if you find another point of view for this problem please let me know, sorry for my poor english.