My fiance and I are traveling to Rome via Iberia airlines from Chicago, we have a connection in Madrid, all I have ever heard about Iberia is that they have a tendency to lose luggage. We are trying not to check any luggage. I have 2 40 liter backpacks and a couple of rolling carryons we will bring with us on the plane. The trip is 12 days, 4 in rome and 7 on a cruise. I pack light, 2 weeks in 1 rolling carry-on
First question is do you think we will have any problem with those?
Second, my fiance has curly hair and requires lots of hair products, what is the best way to get those to rome? Buy travel sizes, ship some to our hotel, or purchase while there?
I am also a platinum member from AA and a Sapphire member with One World, which Iberia belongs to.

Most airlines allow only one carry on per person, so you might will be asked to check in your backpacks.
Lately I have the feeling not only Iberia has a tendency to loose luggage. By now I make sure to have some clothes to change with me in my handluggage.
If she can deal with maybe unknown products for her hair, I would suggest to buy it locally when you are in Rome.
Even for a AA Platinum and One World Sapphire member it sounds like you’re over the increased allowance you’re entitled to. If I were you I would just check a couple of your bags, that way you won’t have to worry about your girlfriend’s hair products. As a One World Sapphire member you are entitled to priority baggage handling. On over 50 international connecting flights over the last six or seven years as a One World Sapphire member I haven’t once had a bag lost or delayed using priority baggage handling although none of the flights were on Iberia. Iberia can’t be that bad, especially when using priority baggage.
I would check the backpacks. There doesn’t seem to be enough room for a loaded backpack in the cargo areas in the cabin. But when you do check the packs, ask them to bag them in a plastic bag. It protects the straps, etc. from being torn by the baggage handlers. I had United do this on their own and didn’t ask Delta to do the same thing and now I have to replace a buckle that got broken.
As far as the hair products, pack travel sized ones in your checked luggage. And then if need be, go to any pharmacy while in Rome and pick up what you didn’t bring. Also, don’t worry too much about your hair. A hat can do wonders for unruly hair!
Good luck!