In spite of what some people are saying, I would rather have a beginner on my horse in a well-fitted port-mouthed or mullen-mouthed pelham than a snaffle (or preferably bitless), as a pelham, like any levered curb bit, reduces direct shock to the bars of the mouth. It does this for two reasons: Because the lever has to turn as it engages, therefore spreading the rein effect through space and therefore time (giving a gentle aid that gets stronger only later in the piece, and a horse can learn to respond very quickly to the gentle beginning) and because the curb chain increases the contact area over which the force acts.
I would never use a jointed pelham: It has a nutcracker effect.
If riding in a pelham, I would use two reins, to be able to separate the curb and quasi-snaffle action. It's not difficult to learn to ride with two reins. You don't have to cross your reins over either: You can continue to ride with the "snaffle" rein running between ring and little finger, and run the narrower curb rein over your little finger and then back through your palm like the other rein, and out over the top of your index finger, with thumb over both reins to hold securely and lightly (which is how we were taught to hold reins in Europe way back).
To make two-rein riding easier, use an elastic band to connect the two rein pairs at the buckled section in the middle. That way, you won't have a muddle of reins to sort out etc.
I really wouldn't use a connector, I'd take it back to the store for a refund. The connector results in the horse being able to evade curb pressure by raising its head, rather than by lowering its head. This is because raising the head with a connector results in the rein sliding along the connector to a point where it is unable to engage the lever.
About (unjointed) curb bits being "harsh" bits compared to snaffles: This urban myth was throughly busted in "Horse Control and the Bit" by Tom Roberts, who runs through over a hundred pages on the physics of different bits and their effects on different mouth configurations (well worth reading this book). If a horse tends to respond better to a particular bit, like a curb compared to a snaffle, it's usually because the bit is milder than another on that particular horse's mouth configuration, not because it hurts more. Hurting a horse doesn't make it stop, it just makes a horse mad.
In Germany, where I began riding three decades ago, it's quite unremarkable to have children riding in pelhams. In Spain, South America etc curb bits are also widely used.
Arabian horses tend to have narrow mouths with little room and jointed snaffles aren't necessarily the most comfortable option for them (or horses in general). It's quite an art getting the most comfortable bit for a particular horse-rider combination.
My late Arabian mare really despised jointed snaffles and took wonderfully to a port-mouthed pelham. This was her competing in (and winning) a bending race when we were both young:
In Australia, pelhams are perfectly acceptable in the show ring, endurance, gymkhanas, etc. Nobody made any objections to my horse's pelham in any of these competitions in the two decades we used it. It's only in dressage you have to work in a snaffle (but you can graduate to a double bridle later). Thankfully you are no longer obliged to use a standard jointed snaffle, as they really don't suit some horses.
If you want to ride with a single rein and a curb, try a port-mouthed or mullen-mouthed Spanish Snaffle (not a snaffle despite the name) with slotted D-rings. You can then clip a single rein into the desired slot in the D-ring, and unlike the connector, or Spanish Snaffles without slots, this configuration doesn't encourage the horse to raise its head to avoid curb pressure. My current riding horse likes this bit better than snaffles - his great-grandmother, with her comparatively wide mouth, was very comfortable in a standard jointed snaffle, and obviously bitless as well (mild padded hackamore with short shanks). Here's a photo of my gelding in his bit, early on in the process of converting him from harness competition to ridden work:
Click to enlarge to see bit details up close. This horse was a stargazer in harness and I was very pleased with how nicely his head carriage improved with being ridden forward into a bit he found comfortable, with very light rein contact. He'd only had a few months of work under saddle there and it was a world of difference already. The rope across the front is useful to stop reins from being thrown over the head in case of a fall, and the horse then stepping on the reins and hurting its mouth.
When using a curb bit, please fit carefully so that you do not trap the corners of the lips or the skin on the chin in the curb chain - and make sure you use a nice flat smooth curb chain, in the groove of the chin, not too high or too low, not too tight or too loose. Check action is correct, from the ground first, by taking the lever all the way through the rotation and making necessary adjustment. Excellent fitting instructions with diagrams in the book I mentioned above!