We just had a large back extension completed. We used a local firm with personal recommendations. We are both out of the house by 7.30am and not back until 5pm at the earliest, so they had keys to the house. It took about 2 months so being off work all that time was not possible.
DH and I had a schedule of works from the builder, which we agreed to, so we were aware of what was happening next. We inspected every evening so we knew where everything was up to. We had regular phone calls and e-mail conversations with the project manager (he preferred e-mail as then we all had a paper trail of conversations).
The works went well, there were little problems that occured (an electric wire was buried under 4 feet of concrete and had to be dug up, a strip light was put in the wrong place) but as we checked daily, these were rectified before becoming an issue.
Prior to commencing works, the builder asked us to keep anything of value (jewellery etc) locked away as he didn't want his teams to be put in the situation of being accused of anything and he assured us that our house keys were kept in a safe in his office, which we actually saw, and were returned there every night.
It is an unnerving thought having people in your home I totally understand that, but it sounds to me like its that or do the work yourself and accept that may/will take an awful lot longer. Rather that trying to co-ordinate all the trades yourself, is it possible to hire a project manager or a firm to manage it all? I assume a lot of work needs doing?
Is there the option of boarding kennels during the day for the dogs? If this is not an option if your dogs can't 'do' kennels, what about a dog minder? an internet search should help find someone. It is unreasonable to expect tradesmen to care for your animals, they are at their place of work doing their job, which does not include keeping an eye on your animals. Sorry.
I hope this helps and gives you some options to explore? Good luck! 