AVE train from Madrid to Barcelona & luggage

[Edited] A fair amount of luggage is allowed on AVE trains but you will have to carry and stow it yourselves. See http://www.renfe.com/EN/viajeros/info/index.html for size restrictions and links on the side for other options. You might consider upgrading to 1st class to be in a car with fewer passengers using the same amount of space and resources, but buy tickets well in advance to get a decent price for 1st class.

The simple rule is you have to carry your own luggage, Through the station, on and off the train, and stash it on the train.
Read this page here: http://seat61.com/luggage-on-european-trains.htm
If you have more than you can carry between yourselves, you have a problem. Some stations have luggage trolleys (for a deposit), but that only gets you as far as the platform. Can you handle this luggage amongst yourselves?

I think the suggestion to use first class is a good one. I use Turista class, and while the cars are spacious, the bag racks usually fill up fast. With that much luggage, you will have to move fast to get everything on and settled. Having a bit more space might help.

That is too much to handle. You really need to rethink the luggage situation. Some of the train station do have porters so someone might swing by Madrid to see if they do. If available they will get you to the train but you have to get it all on and off by yourself. Second, once you arrive in Barcelona you are really on your own. Just getting it all off with the rush of everyone else getting off will be a big hassle. And then you may or most likely not find someone to help you. In Spain access to the platforms is limited to tickets holders so there will not be folks hanging around to offer assistance for a big tip. But that is probably good because you are very venerable to the scam of someone coming along, offering assistance, and asked for a high price for help and maybe a little pickpocketing on the side. In addition you will need to go through a mild airport style security prior to entering the platform for Spanish trains.

A couple hundred euro to ship the two large suitcases home could be money well spent.

I am picturing Atocha station in Madrid. It's huge and usually crowded. Some people find it confusing too. This is one time I think flying might be easier, even though it may take longer. But with all that luggage, the cost may be very high (not even counting the extra taxi costs to/from airports), since you'd probably have to check 2 suitcases each and just take the backpacks as cabin baggage.

Even though it's a long drive (8 hours per viamichelin.com), have you considered renting a car. You could even stop in Zaragosa overnight. Take a taxi to/from hotel/rental offices.

Where will you fly home from? Could you fly from Madrid, leave the heavy luggage stored in Madrid, travel with carry-ons and then go back for the big bags to fly home? (If you're traveling to more than a simple trip to Barcelona) The idea of a car rental might be easiest if you are just getting to Barcelona to fly home.

It's not the amount of luggage - it is the weight. One can easily pull a large suitcase and carry or pull in the other hand the small carry on and wear the backpack. But if these are heavy and/or you are not strong enough, then it becomes a serious issue. This applies no matter if flying, driving or taking the train.

The luggage racks do fill up and so you may be challenged getting more than a couple items at the end of the car. If the carry on or the backpacks don't fit in the overhead rack, you may be sitting with a bag on each of your laps. A 1st class ticket would probably help as the cars are typically less filled ( BTW - it's considered rude in Europe to put luggage on seats).

Shipping a suitcase could be VERY expensive, easily $300-400 dollars depending on the size and weight. SO hopefully you can manage it yourself.

That's definitely too much luggage.

My daughter also studied abroad, but I adviced her to only take what she could manage, which was a 24" roller suitcase plus a small backpack. When I went to pick her up, she had a few extra items, so we ended up sending a package home.
Check for a Mail Boxes, etc. store & they will give you the best deal on shipping your package.

Good luck!

Here's more information for you: http://www.renfe.com/EN/viajeros/info/index.html