The hosts of the wedding chose, for whatever reason, to hire the "official" photographers to document their event. As a guest of those same hosts you should respect the choice they have made and make every effort to accommodate your hosts' wishes. If those hired are less than welcoming and courteous to you, you should still respond to them in a way that respects your hosts' wishes to have them shoot the event! As a professional you should extend the same courtesy to the "official photographers" that you would expect in return were the roles reversed.

It doesn't matter if you think your shots would be better or not! They were the ones hired by your host! Not everyone shoots an event the same way. Not everyone has the same vision for what the final product should look like. Not everyone will think photographer A's photos of an event are better than photographer B's. Not everyone will prefer B's over A's either. Even if it is fairly obvious that the hired photographers are what you would consider incompetent, it is not your job to correct the situation. Your role is as a guest of your hosts, so be a good guest and enjoy the party!

If your hosts planned for you to also provide some coverage of the wedding, then that should have been communicated by them (and verified by you that they did so) to the hired photographers in advance of the event. In the absence of such advance agreements, the hired photographer has every right to insist on calling the shots. Depending on how the contract is set up, they may be charging a minimal shooting fee and expecting to make their income on albums and printing packages. In which case your activities may be seen by them as threatening to significantly reduce potential sales.

The way to resolve the issue is to let the hired photographer do his/her job as he/she sees fit. Period. Regardless of whether or not you agree with the way they are doing it.

Just because you don't feel you are getting in the way of the hired photographer does not mean the hired photographer doesn't feel you are in the way. Perhaps they are sensitive to not stepping in front of another camera to get a shot they need. Perhaps at the reception they have remote "kicker" lights set up and your powerful pro grade flash is interfering with their ability to create the lighting atmosphere they desire (Either by placing extra light where it is not desired or by compromising their control of their own lights). Perhaps they are just a little bit insecure about being upstaged by someone with nice(r) gear, or who seems to be (more) experienced, or both. Whatever the case, as a professional it is up to you to help them do their job the way they see fit. If that means backing down, then (absent of any prior instructions to the contrary from the hosts of the event) the professional response is to back down. It is not up to you to tell them how to do their job when such help has not been solicited. It is not up to you to do their job for them when such help has not been solicited.

Personally, if I am attending a private event such as a wedding as a guest and someone else has been hired to photograph the event I would touch base with them before my camera ever came out of my bag. If I'm a family member or close friend to the hosts of the wedding and they have asked me to shoot some shots to supplement the hired photographers, I would insure before the day of the wedding that the hired photographers are aware of this and are OK with it.