I think you sound like you are not at all in a good place to be quitting MC. I really think letting your H help you find a solution could be both healing and helpful. Don't stop going.
Here is a article from Psychology.com on the subject...
One day I was unable to make my IC session so she phoned me. The conversation felt no different then the ones I had sitting in her office.
The truth hurts, but I have never seen it cause the pain that lies do.
It sounds like you want to accomplish more and need support, so I, too, think you should do your best to find a sitter.
The sessions will probably be more effective without your child - after all, infants call for a lot of attention.
I hope you can work out the sitter - SO you can continue your IC.
It's hard to say how: But you will "KNOW" when it's time to stop seeing your IC...and the time to stop should not be dictated by child-care-issues.
Talk to your IC -Maybe something can be worked out through the IC's office.
Also - check with your local churches; many of them have "Mom's Day Out" services.
I can understand being alone; but I hate being with someone and feeling lonely.