Provided you have your BA Executive Club no. in all of the bookings the AA flights should credit to BAEC and give you tier points. If you've got AA bookings you'll need to put your BAEC no. in on the booking on AA's website, where it says "Add/edit passenger information".

You will get credit for American Eagle flights, whoever they are operated by.

If your international ticket is in business class, and includes US domestic flights, try to book those US flights under an AA flight number rather than a BA flight number. That way you will earn 60 TPs per sector rather than 40. (You'll get even more if you're going to Portland OR but from your East Coast reference I assume you're going to Portland ME).