I've spent almost every christmas of my life on Sanibel and Captiva! Hopefully you guys went to ding darling and saw some of the roseate spoon bills, if not make sure to try that next time! For under 500 I personally have no idea, you can shave a lot off by getting second hand but even then the setup I'm going to recommend will probably still be fair bit over but here me out.
I'm really into wildlife photography and was born and raised on canon- between the 2 cameras I shoot on I'd recommend the Canon SL2 for the following reasons:
It's tiny, its the smallest functional dslr camera that I'm aware of and because its tiny its really light! With that said I have fairly large hands and have no issue using it, my girlfriend has fairly small hands and also finds it comfortable.
Its very beginner friendly, I turned off the guides in the settings because I've been doing this for a while but I checked them out before hand and was impressed with ho well it explained the different settings and modes and how they effect your photo which would have saved me a lot of time when I got my first camera. It also lets you use different lenses unlike small point and shoot cameras which means you'll be able to start with less expensive lenses to see if she like it and if she does then this camera can just as easily attach a 10,000 dollar lens (Although because the camera is so small it does look kinda funny but I can live with that as long as the pictures don't;Hilarious).
Its an apsc sized sensor which means although it has less megapixels and lets in less light (not really noticeable to someone starting out) BUT it (essentially) gives you more zoom. If you buy her lens that goes up to 100mm then it will be more like you shooting a 150 and if she's focusing on birds she'll quickly realize you want as much zoom as you can get! Not to mention
It has wifi! that doesn't mean you can goole on it but it means you can download an app on your phone and connect to the camera via wifi and bluetooth. this mean she never actually has to plug the camera in to a computer to upload her photos. You can do it that way if you wanted to and I'm sure its faster when you want to upload a bunch but if you take a photo you really like you are less than 2 minutes away from sending that photo to your spouse, friends or putting it up on facebook and instagram.
For lenses I use sigma because The canon are really expensive and there isn't enough of a difference to justify the 3x4 times price tag IME. The sigma 100-400 lens is 700 US but asides from the price its a fair sized lens and might be a bit much for a beginner to deal with, they have a 70-300 thats around 300 and like someone else said a 70-200 is a great lens as well. I only have one of three I've mentioned though so I'd recommend you check some reviews on the other ones first. Here are some of my bird photos, 2 of which were taken with a camera set up that cost 3 times as much but you'll be hard pressed to tell them apart- I had to crop all of these because I shoot a higher quality jpeg than what the forum upload feature tolerates so they aren't nearly as sharp as they actually are.
Hope this helps!