Child Displacement - what can I do to help ease the displacement?

Hello,
I recently started a daycare and have a 1 year old (my own) and a 1 year old that I watch. I'm having a hard time figuring out how to keep my 1 year old from being displaced by the whole situation. The daycare child is all over me whenever I show attention to my own child (and I do give the daycare child plenty of attention as they have different nap times- but then he could care less) Any stories on how you've handled this situation yourselves? Thanks! I feel bad for both the kiddies!! I'm sure he misses his mom, but I don't want mine to miss me too when I'm standing right there!:(