What do I need to do to repaint Cabinets in my mobile home?

We painted our travel trailer that had the same cabinet set up. Use a paint/primer called 'Gripper' first and you'll have no problems with the top coat. Of course you'll need to do the prep (smoothing out any rough patches, fill nail holes, etc) then paint w/Gripper & you'll be ready.

The most important step is to make sure the surfaces are clean clean clean.

Gripper is a terrific product for a basecoat on most everything interior or exterior. As stated in other replies, do prep your surface.

Make sure they are clean and dry. Remove the doors and hardware. Mark the doors and cabinets with tape where they go. Lightly sand the doors and cabinets to remove any gloss and roughen the surface for paint with 120- to 220-grit sandpaper. Use a tack cloth or damp rag to remove dust after sanding. Prime with a stain blocking primer like Zinsser 123, KILZ,or BIN and have it tinted to the color of the top coat. This will prevent dark or stained surfaces from showing through the top coat. Acrylic, or water-base, paints are low-fume and clean up easily with water. Alkyd, or oil-base, paints require good ventilation because the paint contains solvents that can irritate your lungs and make you feel sick. Alkyd options require mineral spirits for cleanup, but they provide a hard, durable paint finish. Whichever you use, buy the best-quality paint you can afford for a lasting kitchen cabinet finish. Seal with at least three coats with a water based polyurethane. Use a small foam roller and foam brush for a smooth finish.

The sides are partical board, it's like saw dust glued together. Put some nice contact paper inside where it's peeling. Clean the cabinets with Murphy's oil soap, follow the directions on the bottle. I can't advise you anything else, you need to go to Homedepot or Lowe's and ask for some help with your multi-problem with your cabinets.