Preparing them before you walk through that door is the most important thing you can do, and you are already thinking about it the right way.
At 9 and 11, kids are old enough to understand more than adults sometimes give them credit for, but they still need the information framed in a way that does not frighten them more than necessary. If their dad has visible injuries from the arrest, tell them before they see him. Something simple and calm: Daddy got hurt a little when he was arrested so he might have some bruises or a black eye. It looks worse than it is and he is going to be okay. That one sentence removes the shock of seeing it and lets them focus on being with him rather than being scared by what they see.
On the visit itself, a few practical things worth knowing. Dress them in clothing with no green or orange tones, as many facilities restrict those colors because they match inmate uniforms. Keep metal to a minimum to speed up the security check-in process and avoid anything getting flagged. Bring nothing in that you do not need.
Tell them what to expect in simple terms before you go in. There will be security officers, you will go through a checkpoint, and you will sit in a room with other families. It might feel different from anything they have done before and that is okay. Framing it as a visit to see their dad, not as something scary or shameful, sets the emotional tone for the whole experience.
Let them lead the conversation with their dad. Kids often surprise you with how naturally they connect even in difficult circumstances. Your job is to get them there safely and let that connection do what it does.
You are doing a good thing today.