Mat Leave Concern [ON]

I work for the SCDSB as an EA. We already do not get paid great (vent for another day), but I just realized that due to when my baby is due, (June) I will not qualify for EI once I return back to work (for the summer). I was originally planning on returning to work at the begining of May and work until the end of June. However, this won't give me enough hours to qualify. It wouldn't make sense for me to get a part time job to have some income over the summer, for one, its hard to find a job that will take you for that short amount of time, and my fiance works full-time so we would then have to pay for childcare so I would basically be working for nothing.

I am wondering if anyone has experienced this previously and what they have done? I could go back to work late January to gain the correct amount of hours, but I don't know if my fiance could take the rest of the paternity leave? I am so stressed now and disappointed that I won't be able to take as long as I had hoped for. I know we are lucky to get what we get in Canada but I don't know if I will be ready to leave my baby (FO) at not even 8 months old. I was also hoping to breastfeed for longer than that. I just feel so sad about it now and just want to cry!

**I should have clarifed that I have someone willing to watch my baby from May until the end of June but would not have child care for the summer.