It’s very large and out of control. I think it needs new soil, and perhaps a larger pot. 
Do I put in in a larger pot?

Do I trim it way back?

How can I save it if it breaks completely apart while trying to repair it?

Yes, your plant may greatly benefit repotting in a new larger pot.  Here are some specific instructions:

Repotting

Plants just brought home from the greenhouse seldom need immediate repotting. Many will not require potting for some time. A newly acquired plant must make adjustments to its new environment, and repotting immediately puts added strain on the plant.

A time for repotting is when the plant becomes pot-bound, this is, when the plant’s roots are too extensive for its pot. A pot-bound plant may need to be watered too frequently and may grow poorly.

A good potting mixture for most houseplants consists of a blend of three parts sphagnum peat, one part vermiculite and one part perlite. Many commercially available peat-lite mixes are ideal for houseplants. Exceptions are epiphytic orchids, which should be potted in a very porous medium such as orchid bark, and cacti, which should be potted in equal parts of peat-lite mix and sterile sand. In most cases, avoid the addition of soil to a potting medium, as this often leads to poor drainage, overwatering and root diseases.

Acid-loving plants such as azaleas and gardenias should have at least 50 percent peat moss or other organic material in the soil mixture. With good care, these plants can be grown successfully in peat moss with no soil added.

To avoid contamination by insects, diseases and weed seeds, sterilize soil mixes before using them. One sterilization method is to moisten the soil, cover it with aluminum foil to keep it from drying out while being heated, and place it in a 200-degree F oven for about 30 minutes or until it is heated through. Chemicals for soil sterilization can also be purchased.

When repotting, avoid excessive damage to the root system. Firm the soil gently around the root ball, but do not press so hard that the soil becomes compacted.

Allow enough space at the top of the pot so that water can be added easily. Water newly potted plants thoroughly, drain, and do not water again until necessary.

When to fertilize
Fertilizing once a month is adequate for most houseplants that are producing new growth or flowers. However, plants do not need fertilizer in winter when no new growth is apparent.

Do not use fertilizer to stimulate new growth on a plant located in poor growing conditions. Lack of growth is more often due to improper light or watering than to nutritional deficiencies. In such cases, adding fertilizer may actually cause additional injury.

Drop of lower leaves, overall yellow-green color or weak growth may indicate a need for fertilization. However, these same symptoms may result from poor light or overwatering, so evaluate all conditions before fertilizing more than normal.

Kinds of fertilizers
Water-soluble, complete fertilizers formulated for houseplants are available from many garden shops, florists and nurseries. They are easy to use. Formulations vary, so be sure to follow directions carefully. Do not apply more than directed. The roots of potted plants are quite restricted and easily burned by the application of too much fertilizer at one time.

Never apply liquid fertilizers to a wilted plant. Water the plant first, and apply fertilizer after the plant has recovered and the soil has dried slightly.

Soluble fertilizers such as 20-20-20 may also be used for fertilizing houseplants. Make a solution by mixing 1-1/2 teaspoons of this material in 1 gallon of water.

Some people prefer to use organic fertilizers for houseplants, but either an organic or inorganic fertilizer or a combination of both will be a satisfactory source of nutrients.

Fertilizers that release nutrients slowly or over a long time period require less frequent application than liquid forms. They are available in beads, pills, spikes and other forms. Never exceed amounts suggested by the manufacturer’s directions.

If you would like to read more about caring for houseplants, click on this link: https://extension.missouri.edu/publications/g6510

And yes, you may cut off (prune) longer dangling pieces of your plant so the plant bushes out and looks healthier. The cut ends of those pieces can be placed in a jar of water where they will also establish roots. Therefore those pieces become new plants that you can pot in additional containers of soil.  

Good luck with your houseplant!  It is very special to keep a plant from a funeral, and you have done very well at caring for it.