Moving the database to it's own machine is very common, and if done right should help your performance considerably.
However, I'm worried about your "secure remote connection". Normally, the database should be in the same data center (and even the same rack, on the same switch) as your web server. I believe the appropriate phrase here is "well-connected". When you say, "secure remote connection", I have images of vpn to somewhere who knows how far away. That's likely to be trouble.
If, as it sounds, these two servers aren't so well connected after all, some things you should do to make sure your site remains responsive is check the average latency between them. A quick and dirty way to do this is just ping from one to other so that it keeps running, and watch the times. Mine are almost all 1ms or <1ms, with the occasional 2ms or 3ms. If you're seeing much larger numbers, you might want to rethink this.