A.L.
I have seen them at Petsmart the other day and while I don't have any experience with them and don't remember exactly what they cost, but I do remember thinking that it wasn't too bad.
A friend of mine just got a wireless invisible fence for outside and it works great for her dog. You do have to remember that you have to train the dog for the e-fence though and that will take a while (though your labradoodle may get it quickly).
Personally, we have opted for a cheaper solution to keep our dog confined and have gated off the kitchen with a large baby gate. Our dog doesn't cause any problems per se, but I don't want her on the furniture or chewing up toys my DD may have left laying around - so when we are not supervising her she is confined to the kitchen where she also has her bed and any messes she may make are easy to clean up.
I don't find anything wrong with keeping her restricted to one room when we are not there and when we are around she is with us in the rest of the home (minus the bedrooms).
The one other thing may be medication. If it is an anxiety/insecurity issue some anti-anxiety meds might help.
Good luck.