Kennitz:
it seems lengthy is why I ask.
it expresses a wish of All the best (Wszystkiego Najlepszego), or you can replace it with something else: Much of Happiness (Dużo szczęścia), Good/Much health (Dużo zdrowia) etc.
z okazji = on the occasion (so you just want to use this oppurtunity to wish someone good things for an undefinite period of time)
we use this expression, because the direct translation of Happy Mothers Day (Szczęśliwego Dnia Matki) would somehow imply that you wish her a happy day, just this one day, not much generous of you :)
I guess people don't think of this the same way in English, they simply don't reflect on the sense of this sentence, take it as a standard expression of good will, but in Polish it's not working. You also can't translate Happy Birthday to Szczęśliwych Urodzin (for the very same reason); Szczęśliwego Nowego Roku (Happy New Year) is OK, because you wish somebody happiness for the full year to come (and you can re-new these wishes after 365 days, so they remain valid all the time).
P.S.
Kennitz:
dzenkuję bardzo!
dz
iękuję bardzo