No point in going back to Newport - which is a dump. So, you arrive in Cardiff and see the castle and perhaps go out to St.Fagans Castle & Museum on Cardiff Bus 32. You may also like to take a local train for the short journey N to see Caerphilly Castle. If doing that, on the return, you may like to get off at the first stop after the tunnel (Lisvane) - cross the footbridge and exit the car park - turn L & R into Cefn-Onn-Park = lovely park in temperate woodland. Then resume journey S to Cardiff. Castell Coch is also worth seeing in north Cardiff - use bus to Tongwynlais & 20 minute uphill hike on road.
Use train to Swansea - city in not attractive but has nice location on Bay. What is attractive is the Gower peninsula to the west. Suggest you use Adventure travel local bus to Rhossilli at SW tip of peninsula. https://www.adventuretravel.cymru/
Next, you want to head north - presumably to Aberdovey. You could go by direct train from Swansea to Shrewsbury (via Cardiff, Newport & Abergavenny). At Shrewsbury, you change for a train to Aberdovey. However, there is another way of doing it by train which is cheaper. You take the Heart of Wales train from Swansea to Shrewsbury. This slow train takes about 25 minutes than the longer but faster route via Abergavenny. The Heart of Wales train will be an old (usually single coach) diesel but does go through lovely countryside. https://www.heart-of-wales.co.uk
Another way of doing it is by bus. You need T6 Swansea to Brecon and then you could do it by T4 from Brecon to Newtown where you get the train going to Aberdovey. OR use T14 Brecon to Hereford where you pick up a train going to Shrewsbury OR X43 bus from Brecon to Abergavenny to pick up a train going to Shrewsbury. Don't expect luxury buses on these routes.
Another way of getting from Swansea to Aberdovey is a westerly route. Train from Swansea to Carmarthen - then T1 bus to Aberystwyth - then train or bus to Machynlleth where you change to another train or bus for the short journey to Aberdovey - which might be spelt the Welsh way = Aberdyfi. Buses crossing Wales =https://traws.cymru/en/services
This site should tell you how to get from a to b in Wales:> https://www.traveline.cymru/#
Not a good idea to travel over Easter as engineering work may close rail lines and many things shut down. Even Garden Centres are not open on Easter Sunday even though it is the main planting season.