United Airlines itself only serves Madrid and Barcelona - that's it for Spain.
we are stuck with United since we will be changing our current flights which are booked on United...
Find out if you are really "stuck" only with United, or if you can fly on one of their codeshare or StarAlliance partners. If so, that may open up at least a few more options (Bilbao, Palma de Majorca, Valencia - all of which are served by Lufthansa, an United partner). Going to Majorja would certainly get you some warmer weather...
It's probably also worth noting that the major challenge is just getting to someplace - almost anyplace - in Europe. Once there, it's usually cheap to get to/from where you actually want to be, so if United can only get you to someplace else in Europe, don't assume you can't get to exactly where you want to go without another flight you have to pay for.
I'd hasten to add that doing that potentially complicates your travel (flying on separate tickets exposes you to significant risks if you miss your flight), and would require at least a little more travel time, maybe more than a little - and one of the biggest issues in your first proposed plan that I think many of us pointed out was that you didn't have enough time. So grafting on additional flights would only make that worse. And of course it would be more money out of your pocket. Just saying that it's worth thinking "outside the United box" to consider creative options.
Finally, I'd add this: for most of us, time is our most limited commodity. Yes, we all have budgets and limits, but most of us can usually find more money (within reason), but it's much harder to find more time. If burning a bit more money allows you to have a much better trip, it may be worth it.