I'm looking for a framing crew for all wood construction. 

Note: I'm not 100% sure of the logistics or legality of this but something to consider.Wood Floors:  If you have wood or laminate flooring that you're worried about scratching, require rugs be utilized in key areas.The reality is pets damage is typically doors, baseboards and carpet from wear and tear. 

Is it a wood frame house or block? 

Paint, re-finish wood floors, yard clean-up.

As to the framing repairs, it would likely be most cost effective to rip open the drywall from the interior and then remove and replace the damaged wood framing from that side.

I have a wood-burning fireplace in one of my SF homes.

The picture isn't too clear -- is that cord wood stacked up to the left of the door?

@Glenna Wood I appreciate your input!

If it doesn't have wood to refinish (which you should have lined someone up for floors pre-sale unless you are DIY) LVT is a reasonable choice anywhere.

I'm doing a remodel for my sister who lives in a fancy updated 1980's 3/2 modular and taking out the old kitchen cabinets a crew put the drywall right OVER the existing old original thin wood plastic walls that go in those things.