For about 20 years, I worked as a care provider, either as a preschool teacher/owner or as a nanny. It took a while, but over the years I came to really appreciate what the contract is about: clarity and expectations.
Most parents will appreciate a contract and any other information which lets them know what to expect in regard to payment, hours of operation, what they need to supply (vs what we will provide) and as a nanny, I was clear in defining which jobs were my responsibility and which were the client's.
I think one thing we caregivers have to remember is that, WHILE we all like to feel like one big happy family, this really isn't the case. I think that is the fuzzy area with caregivers, frankly-- we really don't want to rankle that 'cozy family' feeling. That said, it is an artifice which people often create with good intention (and I have worked for families where our relationships extended long past my tenure with them as we are close)-- caregivers really need to strive to professionalize this business, mainly because it is a business. So, be sure that you are doing the business-like things such as creating an LLC to protect your home, should some calamity arise. Talk to your insurance agent about having liability protection, just in case a child is hurt.
Remember, a contract isn't about being 'all about the money', it's about making expectations clear and so that clients know what they are agreeing to. If ANYONE balks at that, it's okay. You really didn't need that client/headache anyway. I've *never* had a parent sign a contract who didn't want to, never had a parent complain. Before contracts, though, I have had a couple clients who, themselves, felt that it was okay to leave me high and dry on occasion-- and it was entirely my own fault, because I didn't assert my needs clearly.
The other thing I know some providers do is to send home "remember, tuition is due/past due" slips early on and then talk to the parent. This may not work for what you are doing; I charged a monthly tuition and ran a preschool instead of daycare. But you may want to consider figuring out if your clients can pay ahead of time for the month instead of weekly. That eliminated a lot of headaches for me. Good luck!