I solve the problem 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>

<!-- 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>

</datasources>

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.