Kathy
There is no export from Premiere Elements (any version) that will give you a file extension .m2ts or .mts. That .m2ts and .mts are file extensions which represent the container format that wraps the AVCHD video and whatever audio compression the file has.
The .mp4 should serve your intended purpose....use of the file for the burn to Blu-ray disc format on Blu-ray dis, copying the BDMV Folder from the Blu-ray disc, and editing BDMV Folder/STREAM Folder's video file (which is a .m2ts file).
But, what we could try (think it will work) as a workaround
1. export your Timeline as you did with the Publish+Share/Computer/AVCHD with presets = MP4 H.264 1920 x 1080p25.
2. at that mp4 export's hard drive save location, then rename just the file extension from mp4 to m2ts or mts.
If you are sending this file to another for the burn to Blu-ray disc format on Blu-ray disc, double check that this person's software supports the import of .m2ts and .mts.
Is the intended recipient of this file insisting on a m2ts or mts file?
Please review and consider, maybe try it as a mini test run. Please do not hesitate to ask if you have any questions on the above.
ATR