Soldering – How to Neatly Bridge to a Ground Plane

Large ground planes, or any large mass of copper make soldering/desoldering more difficult. You may want to look at getting a better soldering iron that can automatically sense load and adjust power to keep the tip at set temperature (e.g. Metcal, Weller, etc)

However desoldering with "standard" irons is usually possible, you just need more time/care taken. Good solder wick and some liquid flux is invaluable, get some of both if you have none already. Flux generously, use the solder wick to remove as much solder as you can (often with care enough can be removed to free the lead with no further heating, but almost always a little remains however you remove it) from both pads, then if any remains, heat the pad until solder is melted, then wiggle component gently and lift that side slightly, do the same with the other side to bring level, and repeat till you gradually work the component out.

One "trick" if solder will not melt due to too much copper is if you have another iron, you can try using two irons on the same joint (may need someone else to hold the other iron) but this is rarely necessary, and certainly not an alternative to getting a decent iron.

As SubZero says, if the leads come out you are certainly pulling too hard - with some components this happens more easily when they are hot, so a heatsink clamp on leads (e.g. pliers, which can be used to pull lead gently and avoid stress on body, or a dedicated clamp can be bought) is sometimes a good idea if possible. With patience pretty much anything can be removed. If you are planning on doing this a lot follow his advice about the hotplate and heat gun (soldering type, not paint removal type)

Are you using solder paste or just soldering by hand?

First fill the vias with just enough solder that the holes are filled. You don't want solder above the surface of the holes.

If using solder paste, add paste on top of and in the space between the vias as well as the lead pads.

If soldering by hand, add lots of flux on top of and between the vias. After soldering the leads to the pads, turn the board over and apply heat to the vias. The idea is to reflow the solder in the via holes onto the thermal pad.