How to replace door moulding due to dog damage.

Go to your home improvement store and take a picture of what you have and they can help you get new pieces to replace it. I would go with what they suggest to not have the problem again.

I would try to cut/sand the bad parts, fill it with wood filler, and paint it.

AHA! Particleboard with a paper/vinyl covering. Swells when it gets too wet. That is a complete door jamb. You don't want to replace the whole door jamb or just that side. Use a putty knife or chisel and scrape off the swollen part. It will crumble. Use wood putty to fill in the area. Let it dry. Sand it smooth, then prime, and touch up paint.

Okay James, is "swole" really a word?

Scrape this down until everything that sticks up and shouldn't is gone. Product to use is Bondo wood filler, a hardware store item. Just as the name implies it is at it's core auto body filler. Mask surrounding area carefully.

This will be a bit of trouble to shape once the Bondo has hardened but a sharp wood chisel will be a lot of help. You just have to carve a new door jamb out of the filler you applied where the old one was missing.

Replacing the door jamb would be a better repair, especially since yours is made of sawdust and glue, but hanging a door I consider to be a more advanced woodworking than most homeowners care to tackle.

You just carefully pop it off using a thin blade of some sort and go to Home Depot Lowe's Menards one of those stores to see if you can match the trim work and if you can paint it or stain it to match and put it back up with finish nails

I have done this repair on exterior doorways a few times.

Depending upon how extensive your wood rot damage is you can chip or chisel out the old rotted wood and if minor in size for replacement we use the epoxy stick. Or if it’s a larger area of damage, the area needs to be removed and patched with some replacement wood.

Sand paint and caulk and hopefully your repair will be successful.

Heres the epoxy stick thats great for patching its a bit more structual than bondo.

Putty characteristics

Steel-filled material, mixes in your hand and hardens in minutes

Suitable for plastics, metals, fiberglass, concrete and ceramics

May be drilled, tapped, filed, sanded, sealed and painted when hardened

Non-toxic material contains no solvents

Will not shrink

Consider the epoxy putty for your repair needs. You cant imagine all the different uses for repair and rehab!

https://www.oatey.com/2373255/Product/Oatey-Fix-It-Stick-Epoxy-Putty

If it were me, I'd sand it until it wasn't swollen anymore, place joint compound over the entire area. After it is completely dry, sand until the door opened & shut smoothly, then repaint the entire thing. Repainting one area never matched completely & if u repaint the whole thing it will draw people's eye up and not down to the spot that doesn't match.