admylin the casual and dismissive attitude of your dd's school sounds incredibly frustrating to say the least!
lannook I second the point that many toddlers groups close (rather annoyingly) in the school holidays. Most toddlers groups (around here anyway) are in the morning, with the deliberate idea that mum takes toddler while any older siblings are at KiGa or school... But you may find an afternoon one, less likely though. I'd still look for one to take your 2 year old to in the mornings as they are a good way to meet people - who you then might spend the odd afternoon with. When we arrived here my oldest was 19 months and I was pregnant with my second, so I had a year with both of them with me full time before my eldest started kindergarten, and I joined the local German toddlers group (despite next to no German - if you join a small group they are friendly I found, you will feel a bit lost at a big one without the language). I also eventually found an English speaking group, through which I met the only 2 English speakers I am in regular contact with now (stopped going to toddlers when my youngest turned 3 and started KiGa).
In the afternoons playgrounds are the best bet - talk to people, encourage your dds to play with other kids (sand pits are great for kids mixing - take disinfectant gel if your also going to give them snacks though due to the possibility of cat poo...). I also found out about the toddlers group I joined by asking mums in the local playground) Friebads (open air pools) are also great - they have toddler pools, and are perfectly manageable on your own with 2 toddlers - I've been every summer with my kids as they've grown and still go with 2 very active under 6s and a small baby. Maybe you'll hear another mum speaking English to her kids, in which case say hello (have also done this - you don't know if you don't try!). Also try Badsee (swimming lakes) to pass the time on a hot day - just pick your spot near other families for safety factor. On a cold/ wet day or to get out of the heat most libraries are quite child friendly, some even have story hours (does no harm to build up the German) and at 2 and 3 you can just tell a story from the pics if they have no English picture books. When mine were 1 and 3 we used to go to the local library every Tuesday afternoon (it's open limited hours).
Soft play places do exist here but are called fun parks - do a google search under funpark and your postcode, in my experience they are bigger and more expensive than average UK ones but also far more thin on the ground - avoid in school holidays but are a good occassional treat on a weekday afternoon in term time.
Hope to help!
Oh apart from that just have to say Henry has hit a really cool age now - rolling everywhere and giggling and laughing, I do love it when they start to do stuff other than cry, feed and poo! :) He'll be 4 months on Friday! Time is flying :(
Ah yes and the reason I actually logged on - DD wants a cinema party for her 6th birthday, to see the new Lilliefee film. Her birthday is on the Monday of the second week of term and we have sent invites out already, to get to the cinema at 3.15pm on a Monday (Monday is ?2 cheaper per ticket and also her actual birthday). One mum has said the kids won'*t be finished with their homework by 3pm! I suspect she wants me to re-schedule to the weekend for her own convenience tbh from other things she said, but is the 3.15pm start really going to be a problem, given school finished between 11.30am and 12.30pm (depending on the day). Advice from mums of school kids - first class homework won't take over 2.5 hours will it?