Firstly use your Alvarez, miking up outside will give you all sorts of problems and you will get much higher output levels by plugging in.
Secondly, you haven't said what parts of the day you are playing - ceremony only? I did a wedding ceremony last summer, outdoors, same size as yours, using a Roland Cube St Ex, which was fine in terms of power output and it's less powerful than your 80w amp (you need to think about power though, I don't think the Cube 80 runs on batteries?)
I should stress this was for the ceremony only, when people were seated together in a small area, very quiet location and were fairly quiet themselves - taking their seats, during the bride's entry and during the signing of the register. Afterwards I played during the drinks reception/photos when people were spread out across the castle lawn, noisier, drinking and chatting, I used my 300w PA for this, speakers up on stands, as the Cube would have been inadequate - if I had been booked for the meal I would have used the PA for that too.
So unless there is something different about American wedding ceremonies I am sure you'll be fine with your gear for this one-off family event where you have not been hired as a pro. Getting your amp up on a stand/chair will help, as will Toms tips above about placing it near the audience.