There are lots of pros and cons to owning your own pony, the pros are kind of obvious but the bond and enjoyment a child gets from their own pony is second to none and it brings on their riding no end as well. The cons unfortunately are extensive too though, the cost is a big one, £200 pcm for livery sounds incredibly cheap (I pay more than 3 times that!), I assume that's for DIY? That does mean a lot of work and it will almost certainly mean you doing a lot yourself (as your DDs are way too young to be much help) and the amount of time horses absorb is the biggest con to ownership IMO, time spent riding is the least of it (and 2 times a week is probably not enough for most ponies, especially if s/he has to be stabled overnight in winter so if that's what you can realistically manage you probably need to look for a sharer to fill in the other days). It's easier in summer when hopefully the pony can live out but even then it'll be 2 x visits per day (unless you can team up to share jobs with someone else on the yard) to ensure they have water and haven't killed themselves, in winter it really is a hard slog, mud everywhere, cold, wet and lots of carting hay and water around and mucking out is my experience (around here on pretty much every yard the horses have to be in overnight through winter), even a very keen child loses enthusiasm for going to the yard after school in those conditions and has to be jollied along bribed to help out... people say this about getting a dog but I think it's a helpful exercise for a horse too, don't get stuck in your imagination on the lovely sunny days when the kids will be having fun cuddling a lovely pony, imagine the very worst day when you/the kids have colds, bad day at work, there's homework to be done and the house is a tip, it's pissing it down and pitch black by 4pm but you have to get up to the yard to feed and muck out, still up for it then? If so then you are probably ready 
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Also as others have said I'm not sure the pony you mention is the right match right now, we have a saying in the horsey world 'green on green makes black and blue' ie a novice owner and an inexperienced pony is not the best combination, clearly your DD is a good rider but are you horsey yourself? Knowledgeable and confident enough to tutor her through the inevitable ups and downs of bringing on a green pony? Has your DD ever ridden on her own outside lessons, without the teacher telling her what to do? What about your younger DD, can she ride this pony too and if not does that just mean she can't ride at all? I get that pull towards a pony you already know but I would incline to look for an older, been there done it type, I think 12.2hh is about right, you could go a little bigger but I'd rather have confident and happy in the here and now than overhorse them with too much of an eye on the future, a sturdy 12.2 could well do her for 4 or 5 years yet provided she doesn't get too tall too quickly. OR, and this is probably a better idea still, I'd keep up the hunt for a share pony/part loan. This is honestly so much easier in terms of commitment both time and financial, gets them used to riding without supervision and much more flexible if they grow quickly or the pony doesn't suit as you just give notice and look for something else rather than the whole hassle and heartache of having to sell. I bet if there are new liveries coming in some of them would be up for having 2-3 days a week of work taken off their hands and/or a financial contribution, esp if your elder DD is known as a competent, confident light weight rider... maybe ask about putting an advert card somewhere on the yard?