I think you just need to over come the fear of leaving them with someone else! Sounds like a great plan, hire someone now to go to the park with you. That should build your comfort level so when you do need to leave them you trust her and the kids do to. Also, should this pregnancy actually become high risk you have a plan in place.

My pregnancy with may daughter involved weekly appointments. I then also had biweekly ultrasounds from about 24 weeks on. Ended up on bed rest from 31weeks (contractions every 3minutes round the clock) and had her at 35weeks0days! So glad I wasn't trying to do home daycare at that point in life!

I suspect once you get to know the person and once you NEED to go to the appointments you will be less concerned about the 'what ifs'!!