I know I'm not responding to your question directly.. but without first reading the other responses my first thought was.. if you already have an 'extra' carseat to use this one as the back and forth seat. (or your husband if he is the main transportion person, yours would be the extra.)
so with out more details it almost sounds like one of you drop off and the other picks up and it seems more logical to have the babysitter have one. And it is not fun really to transfer the seats. but as the other gal said.. just put it on you/ or husbands 'to-do' list for the babysitter on that day :)
I did actually read all the posts.. and they have some great ideas.. here are some thoughts.
Wait to get the 'extra' seat until it is always forward facing.. * they are a bit less expensive * not so bulky.
&/or find a friend whose baby is just graduated out of their convertable & ask to borrow it for a few months.
by the time you might likely finish your research on this you would be ready for forward facing.. (~ 12 months,. unless your 10 mo. old is small)