Any lens 50mm + will make a nice portrait lens, although I've never hired a lens out so my advice may not be much use to you as I've no idea how much they cost.
At work, I generally use either a 60mm f/2.8 G(macro as it happens, but an awesome lens), or a 70-200mm f/2.8 G. They're really easy to make an interesting shot out of nothing (and let's face it, 90% of a wedding is sitting around); use selective focus (wide aperture) and pick the 'important' people out of the crowd. We use this method a lot for VIP visits and the like, and they always get published. The downside is that if you're limited for movement, you'll struggle to focus with such a long focal length and will miss the wider action.
As with any photographic job, I'd say you need a variety of lenses which allow you to work around the subject, although I'm realistic enough to realise that you don't want to spend hundreds of pounds on hiring kit, particularly as I would assume you're not getting paid with it being family?
With that in mind, I wouldn't worry too much about it. You have relatively low pressure on you in this instance as people won't be expecting high-end images as they would when they're paying £2k for a photographer. They'll be looking for images of themselves, family etc, and you don't need high-end kit to take these. Personally, I'd look to get certain group shots which you know will be the ones people will want. (A large group of the whole family, smaller groups of the groom and friends, mum and close relatives etc etc). Sometimes at work I'm stunned when I've spent hours taking artistic photos, trying creative lighting etc etc, and then the subject will often just pick a simple image of themselves which I considered a snap. You have to remember that not everyone is a photographer, and so doesn't see the world in the same way as you might do.
I wouldn't worry too much about it, just relax, try your best and see what you come away with. Having a pre-planned idea of a few shots you'd like to try before-hand is always a smart move, but remember that sometimes your best laid plans will go to rat-****** and so always remain flexible. I'd agree that trying to remain neutral and not get too emotionally involved in the day will help you capture some of the more photogenic moments, but when all said and done, it's your mums big day, so do whatever it takes to make it a good one for her, and that involves putting the camera down and having a drink with her at some point!
