They're usually easy to repot with normal care being taken. The 'smaller off-shoot' is a new plant. That can be separated once it has developed its own root system. Don't cut it off before it has the roots as it will most likely die. Those Philos are different from some of the other species that grow readily from cuttings.

There are numerous plants sold under the name "split-leaf philodendron so if you can either post a picture or link we can better give you the info you need.

Generally;
If it is a "tree" type philo then tropicbreezent's advise is right on mark. If it is a vine-ing type philo then there are a couple options you have. You can take cuttings from them and increase your chances of it surviving.

Tree types can be dug up from the ground and potted. The following can be applied to either types. Dig around the plant a couple of feet or more around the base to loosen the roots, A gardening fork may be a better choice of tool then a shovel for this. Gently remove as much of the soil as possible because the soil from the yard isn't going to be a healthy soil in the pot. In a pot you will need to have a loose fast draining mix, The top soil from your yard will soon become dense and compacted in a pot and smother the roots and then they'll rot.

Make sure the barrel or whatever else you decide to use has plenty of holes in it for drainage, you'll want the soil mix to be able to stay damp but not wet.