As your quote above states, I too think the way I was brought up was fair and the RIGHT way. DH thinks the same about his up bringing. We've learnt to compromise!
Is the timeframe they gave you workable if you gave them the breakdown, ie:
Be here at 5pm (or whatever time is suitable), yuo can help bathe & put DD to bed, or bedtime story or whatever it maybe, DD goes to bed at ??? time, and wont sleep with people over so could you maybe gone by ??? time.
*also could you try and get DD used to lseepign with ppl over, that way they could stay after DD has gone to bed for dinner, or a catch up?