We have moved ourselves twice (once when childless), and had removal companies for 2 international moves and 3 in this country (one just across town), all when having fairly small child(ren) and one when 2 weeks from due date with DD.
For all the professional moves we had a packing service - it was provided for the first international move and it was SUCH a joy that we have always paid for it since.
Nothing has ever been broken during the professional moves (and if it had, their insurance would have paid for it, unlike if we had packed or moved it), and the 'do it all in 1 go, get it done, get it put in the right place' slick professionalism of it was a total joy.
We have never paid for an unpacking service - though it was included in 1 of the international moves, and when I was highly pregnant they did reassemble all the big furniture for us unprompted -0 and that was great because it allowed us to judge what small items went where as needed [and to put unpacked boxes into the spare bedroom and shut the door for 3 montths when I went into labour].
On the other hand, moving ourselves was long, stressful, boring, inconvenient, dirty and very grumpy-making.
If your DH won't back down, then get the removal company to do everything except his clothes, and his garage - and he needs to pack and move those, you won't be involved. The piano will be better insured with the removals company, so I would get them to do it, though they will probably itemise it out separately in the quote.