I don't understand what you mean by "give way" - did the bike tip over due to inertia and/or a high center of gravity, against your efforts to stabilize it? This can happen when you are standing on the ground and not on the pedals, depending on where you are holding the bike, and what fulcrum exists (e.g your leg against the frame) below the center of gravity that could work to flip the rear wheel sideways and off the ground.

When your body weight is on the bike the, all that force against the ground and your tire traction will prevent the rear wheel from flipping sideways or up. The bike handling will feel weird if you stand up out of the seat - the frame will have a lot more lateral inertia when you try to lean or turn quickly, but you probably won't notice anything when you are sitting unless it's a particularly heavy load or it is positioned high on the bike.

If you are attaching things to the sides of the rack, real pannier mounts are recommended rather than DIY straps.