At this time of year and after the recent rain the very best option is to head for the coast. The top course in Cumbria and the best value is Silloth-on-Solway which is about 45 mins easy drive from Center Parcs. You won't even have a speck of mud on your shoes afterwards. The course is superb for all, but "occasional" golfers will struggle, especially if it's windy.
Keswick will pssibly be far too boggy, Penrith will be fine unless there is more rain,ditto Windermere. It is too early for Carlisle and Eden to be at their best.
Penrith GC is only 5 mins away and Appleby only 15 mins. If you're stuck for time these are your best options. Penrith is more manicured but Appleby has much better greens at this time of year.
Let's know what you decide and how you get on !