If you have got to get from llangollen or NE Wales to the south (Cardiff &/or Bath), then you may well consider driving down as there are plenty of places that are of interest. The A5 from Llangollen to Shrewsbury is a reasonably good road - in fact, from the canal, you may well going this route at Chirk. Then, it would be the A49 going south to Hereford. This route can be slow going and Hereford is prone to congestion. On the A49 route, Stokesay Castle is well worth a stop - really a medieval Manor House. 1 mile S of Stokesay is Ludlow - well worth a look though castle is nothing like as grand as those in north Wales. If heading to Bath, continue south towards Monmouth and then follow A466 down the lower Wye Valley. The main place of interest here is Tintern Abbey (ruin) - then over the Severn Bridge and on to Bath.
If heading from NW Wales to the south, the A470 is the route to take and this is more scenic than the route already mentioned. You could skip Cardiff and travel via Talgarth and Crickhowell to Abergavenny before hitting the A40 expressway to Raglan (Castle) and A449 > M4 to the Severn Bridge. That is not to say that the Cardiff area is not worth visiting - it just depends on how you wish to allocate your time. (The kids might well like the ride on the Llangollen steam railway - which goes through some lovely countryside).
You could travel by train to Bath or Cardiff. From the Llangollen area, the nearest point to pick up the train is Ruabon or Chirk. Direct trains also run from places on the north Wales mainline to Cardiff & London. Chester is well worth a visit and could be done by train.
If going from north Wales to Bath, you can travel down the line that goes via Hereford & Abergavenny to Newport - where you change trains.
Mention has been made of Tenby - which is a lovely coastal town in Pembrokeshire (SW Wales). This would however, be going way off in another direction. All well & good - if you have the time to drive down the western side of Wales.
Look at this map of Wales and try and ‘street view’ the routes/places mentioned to try and figure out what is right for you. (Also google the places mentioned). https://email@example.com,-3.3043975,9z