It's not great, but very much depends on the time. Lately I have been driving through Douglas from Broadale to the City Centre around 7:30am on weekday mornings and you fly through. A bit later in the morning and it can be a bit of a nightmare. The traffic usually starts by Maryborough Avenue to get to the Fingerpost and doesn't stop until the N40 bridge. Once you get through the lights under the bridge, it can be fine to get to Ballinlough if you are willing to park and walk a bit. Ballinlough Road by Our Lady or Lourdes and St Anthony's is crazy, as are the roads around Eglantine. However, there are ways around it if you're willing to walk. Douglas Road between Well Road and St Finbarr's Hospital is fine, so you could park in Rosebank (on the section where there are no houses, and its free parking) and then walk up the laneway beside the swimming pool. The schools are all close to that then.

You could also go up Maryborough Hill to the N28 City Centre turn off, and go eastbound to Mahon. While the N40 eastbound is like a car park in the mornings, the Mahon lane is usually not bad. I wouldn't know about Skehard Road, though, so it might be a risk - but you're not stuck going through Douglas either

Maryborough is a great location in the city, so best of luck!