1)You can't book Thomas Land Express Bus at the moment.
They says it is temporary but it's been already a year since we can't book that bus.
But, 1 positive info for you... departure time : 08:15 - no.1 bus is highly possible Thomas Land design!
2)I don't think you have to queue on the line so much at the entrance even though it's a holiday.
But I recommend you to book online in advance because you'll take your children with you.
You can book online from here;
Choose "トーマスランドパス引換券" then click "選択する".
Choose 2 from the pull down box of "トーマスランドパス引換券 中学生以上～６４才"( adults), and 2 from "トーマスランドパス引換券未就学児（３才～）" in the same way, then click "申し込み".
Click "チケット予約へ" on the next page.
Fill up your e-mail address and phone number( 10 or 11 digits without "-"), then "次へ".
Fill up "マイページログイン用パスワード", 4 digits password for confirmation.
Confirm your booking status in the next page, and if it all right, then choose right picture from 4 items and drag & drop under "アイテム認証". ( This must be difficult part for you. Please google the word turned RED into English then you'll find the you need).
There are no choice that you can finish your payment by your credit card for this ticket.
So please stop by Lawson ( a convenience store) and complete your payment after you arrived in Japan.
Please check below how to pay at Lawson;
3) Don't worry, there is a place for them inside the bus.
Ask when you check-in, or get in the bus that you need the place for your strollers.
Hope this can be your help, and always welcome for the further questions!