Hi Tommy girl,
I second all the opinions on Fishguard. It is a dumpy port town. There is absolutely nothing in it except 2 average supermarkets and they are the most exciting part of it, everything else is grey and grim. When you get there you will agree and will want to leave it at full speed.
Could you see if a taxi service would be available when you arrive? There is a decent-sized market town called Haverfordwest about 25 minutes away. I see that they have car hire options open during the Easter weekend.
If you manage to hire a car you are in business. The coastal area of Pembrokeshire is beautiful. Tenby is a fine town, beautiful Regency-type houses, it gets crowded with tourists but has lots of facilities. Its a real bucket and spade coastal town. If you get good weather the town's two fabulous sheltered sandy beaches would be nice for the kids. There may even be a festival or two on.
Bluestone Resort in Narberth is not far away. It is a self-contained holiday resort with a lot of space. It has high quality self-catering accomodation (lodges) and is especially suited to families with children under 10. There are plenty of activities for the under 10s and a largeish Aquapark, and then you have the option of paying (handsomely) for others activities if you like the sound of them. It is a Welsh version of Center Parcs if you are familiar with the concept. You would have to book from the Friday to the Monday.
They have a touchy feely website with all the details. On perusal this evening it would seem that the 1 or 2 bedroomed lodges -accommodation are booked out. And they are horrendously expensive online. However, my tip would be to ring them up directly. They often have cancellations and their over the phone rates are half of their online rates if they want to make the sale. At least that is what it was with us.
Hope this helps.