I feel your pain, for sure!! I did feel like I got sick more when I first started doing home daycare. In fact, statistically when a child starts daycare they get between 7 and 10 viruses the first year. That likely could apply to the provider and their children, too. It will likely get better, though.
Don't freak yourself out too much, though. As long as you are being clean in the general sense of the word, you can't do much more. Remember that we have immune systems for a reason, and going overboard with antiseptic, antibiotic and so on cleaners can actually be detrimental in the long run.
When it comes to kids mouthing toys, my personal choice is to teach them that it's not something we do anymore. I understand that it's a normal part of child development. But past around 12 months it's not necessary. I ask for parents help in ceasing this behaviour. I have a section in my handbook that discusses our mantra "ONLY FOOD GOES IN OUR MOUTH". It's just good hygiene when in a multichild care environment. Some kids do it more than others, but with a little persistence, you can begin breaking those habits.