My website averages 3500-4000 unique visitors but I'm only making $5-$20 per day

Then how are you generating revenue? If it's Adsense alone 3500-4000 visitors a day won't cut it. Adsense only pays you per click. The general rule of thumb is $1 for every 1000 impressions., thought it can be much higher or lower depending on how often visitors interact with ad content.

Hi there vmustang, you must increase your traffic into your website through investment traffic because it is targeted..I highly recommend to dive in at Facebook because in there you can use the Facebook Advertising.

Looks like there is some good potential there. Just tell me a couple of things:
1. Are you writing these posts?
2. Are you making these $5-20 just from the Adsense ads I see there?
3. Are you making any money from your Amazon store?
4. Do you really only have 283 subscribers? If the answer is yes, then this is where you should start from.
5. Are you making any money from your email list?

So, to reply your initial question it's not a design or technical issue. What you need to do is increase your conversions rate by the following ways:
1. Increase the number of your subscribers. Where your subscription form is located, it is almost impossible for someone to find it. I could double your subscribers' number in one month. Just a single month!
2. Start making money from your email list. I know that you probably do not agree with this, but there are hundreds of ways to do this, without making these people feel like they are being spammed. Just design your campaigns carefully and you can make some good money, without making your subscribers feel spammed.
3. Replace your Adsense ads with targetted ads of businesses who sell products for pets. You should actually try to sell your website ad space. Just email a couple of companies that sell products for pets, send them your Analytics and you will make multiple times the money you make from Adsense.
4. Remove your store, or replace it with one that would bring you some sales.
No need to use the money for yourself. But by making more money you can invest them to get more traffic and reach more people. You can also use them to promote your goals.

I also checked your FB page. Huge potential there, too.

Hey, I think the logo could look more animal-lover appealing, and the website currently looks more like a blog. I think if you made it easier for people to navigate around and or support it you'd get a potential increase in revenue. Simple design is the key to an user friendly website.