I only have status in united lounge and amex platinum lounge.

I did consider a train but with a kiddo in tow I don't know if I would get lost. I am very bad with directions. There are many transfers right? I will be a most lightly to miss transfer stops if multiples are needed probably half asleep when i get off plane. I am not familiar with london at all. I researched it . It looks so hard. Is it?