We are planning a trip to Scotland in late April/early May 2018. It will be a self-tour car trip. I have our Scotland trip pretty much planned out but I really, really want to see Hadrian's Wall and Warkworth Castle in Northern England as well. I would go so far as to say Warkworth Castle might be my #1 destination with #2 being the Orkney Islands and #3 the Isle of Skye. That being said, I need input from all of you UK travelers or citizens as I have never traveled to the UK before. Is this something I can do in 17 days (Travel days not included. Entire trip will be 19 days).
I am not opposed to flying in to Northern England and flying out of Edinburgh if necessary.
Depending upon what else you are planning to see/do in Scotland, it's possible. Having done both Orkney and Skye just bear in mind that since most of your travel will be off of the main motorways, it will take you longer to get from Point A to Point B so you need to figure that into your calculations.
To add Warkworth Castle into your itinerary, I'd look either at flights into Manchester - if that's not feasible, you could fly to London, take the train to Manchester and pick your car up there. It's about 3 - 4 hours to the castle. Edinburgh is about another 2 hours so you could stay around the castle or push on to Edinburgh. Since this is your first trip to the UK, I'd recommend staying around the castle and then going on from there - driving on the "other side" takes a little getting used to and since it's the absolute start of your trip, you will be jet lagged.
As I said, it really depends upon what all you plan to see/do in the Highlands. I'd recommend a minimum of 3 days for Skye and 3 days for Orkney. Absolutely gorgeous parts of Scotland and well worth the effort to get to!
17 days is plenty of time to see Scotland and the parts of Northern England you've mentioned. Some people expect to see 3/4 of Europe in that time frame!
The obvious entry point for Warkworth is Newcastle airport – plenty of flights via major hubs such as Heathrow, Paris and Amsterdam. But why Warkworth – it’s OK but Northumberland abounds in ruined castles.
So, fly into Newcastle and out of Edinburgh - easy peasy.....
As the others have said, 17 days should be adequate. I can't speak for the Orkneys, but Hadrian's Wall is awesome. If you can, allow a full day for walking the wall. You might look for a B&B in one of the towns north or west of Newcastle and spend one day at Warkworth Castle (perhaps also including a stop at Alnwick Castle?) and another at the Wall. You are then a fairly short drive away from Edinburgh. From there, head for Inverness and onward to the ferry to Orkney. You'll have to backtrack a ways from there, then follow Loch Ness to Fort Augustus where you turn off toward Skye. After Skye, you could either drive back to Edinburgh via Fort William and Glencoe or retrace the way via Fort Augustus.
Naturally given the climate and time of year, dress in layers (including long underwear) and use waterproofing products liberally on your footwear and outerwear before leaving home. Cashmere sweaters are ideal because they're warm w/o bulking up your suitcase. I found fingerless gloves and a rain hat essential.