SarahMc - you might be lucky if you ring hotels directly esp. if you can go mid-week and stay out of school holiday periods.
As a lone parent, I found the best solution for holidays at home when they were small was the trusty caravan, excellent value for money in terms of accomodation. The money saved on hotels meant I could afford to pay for sailing/windsurfing/horse riding and the like. More importantly (from their perspective) was the ready made supply of friends in the caravan site.
If that's not an option for you; you could consider Youth Hostels (An Oige), many of them have family rooms you can hire and often have en-suites etc., Hostels in the UK and Scotland are very good - NI in particular is great value for a short break. Becoming a member is cheap and they have discounts for lone parents.