If you are arranging by text, then a quick "reminder" text won't look too pushy, especially if you word it as if it's from your dc (ie just wondering if you had thought anymore about the 29th, as dc is pestering me about seeing your dc).
otherwise how about trying a phonecall, because that can't be ignored can it? just a quick chat and then, once you've ascertained that its an ok time to talk, ask them if they've got their calender because your dc would like to have theirs over to play (or vice versa) - that way they can't really say no.
I don't think anyone - or very few people - will ignore you out of nastiness or cruelty. It really will be that they forgot, or something else came up, or they are meaning to talk about it with their dp first, and a reminder text will push it back to the forefront of their mind.
I know, because although I am fairly outgoing (as in the not shy sense) an fairly organised, there are still a few texts that i've not replied to yet, which i've been meaning to reply to for a few days, but, well, life got in the way
Oh, and whilst a phonecall might be very very hard for you as a shy person, the other person receiving the call will have no idea you are shy, and will treat you nicely (I promise)
HTH