Say I have someone booked for daycare but I also have someone booked for walking/drop-in on the same day, am I supposed to take the dog I have in daycare on the walk/drop in with me too? Or should I not schedule them on the same day?
When I have new daycares I always crate them while I am gone. For clients I have had before and feel comfortable with I leave the dog out to play with mine. I wouldn't ever bring a daycare to a dog you are walking. I also don't feel it is necessary to inform the client when you leave your home unless it is for an extended period of time. Most owners know you have things going on and will have to step out at some point.
I think the best advice is to be transparent to your clients. Some have different expectations than others. It's easiest to juggle when these are repeat dogs and you know their preferences well.
Yes, it's possible to communicate this, so you can do a nearby walk and have a happy daycare client. Some people book day care because they don't want the dog to wait too long in between walks, and don't want to give access to their home to someone. In those cases, you could ask if the client would mind if you left their dog safely inside your home while you walked another dog and let them know an approximate length of time you'd be away. If the dog doesn't have separation anxiety which results in them needing constant supervision, they may be fine with you leaving them for an hour or so to walk another dog, so long as you took steps to ensure their safety and comfort (i.e. dog-proof environment & walk before you go). Generally, that seems safer than taking the dog along - although there are exceptions. Many dogs that stay at their home and are walked may not do well with another dog joining. There are some people with well socialized dogs who book walks rather than day care just because they don't have the hassle of drop off/pick up and it costs less. Those clients may be fine with another dog coming, if you can safely walk all. I'd recommend discuss your plan ahead of time with all the clients involved and listen to their input.
I don't do any traveling services. However, if I were a client who booked daycare I wouldn't want my dog left alone. Isn't that the point of sending a dog to daycare, i.e., that he/she is attended during those hours. Unless you have someone else at home for daycare, I wouldn't book any traveling services at the same time.
Under no circumstances would I take a client's dog along to walk other dogs or do drop-ins.