I do home childcare as well...and do like when children learn to self soothe, but not all parents are prepared for this, nor are the children. I am willing to work with those parameters as much as I can.
In MN, we are NOT allowed to let a child sleep in a swing. Its not safe and agains SIDS protocols. If they fall asleep we are instructed to move them within a few minutes.
I have a new best friend in my daycare. I haven't had small small infants in about 2 years..they have all been older 6-8 mos when starting or older..but this week I started an almost 3 mos old..and will have another next month. I bought a Moby Wrap. I ahve had carriers and packs of all sorts in my 13+ years in home childcare and many more years as a parent s ananny before that. They always pinched and poked at me and hurt my back. I am LOVING this Moby Wrap for soothing this baby and being hands free. This will help me do my own sleep training when the time comes. For now she is small enough and I can carry her to sleep or soothe her to sleep, attachment-style, and when she is good and out, I can carefully undo the wrap and lay her in her crib (can you say REM sleep! Little sucky lips and all! Love that!)
I agree with other posters...guiding parents with Their child decisions is tricky. Carefully offered experience notes...this workes for me here items, etc are what is called for...then figure out what works at your place. You can not control what they do at home, but work to establish what the child grows accustomed to at your home or a plan you and the family can agree to while in your care is what is best. Its what works for me.
Try the Moby! I got mine at Target for $40..tax write off..very comfy (takes a little practice...I used some big dollys and stuffed animals before she arrived!)..but I LOVE it!
Good luck!