Help in selecting the Travel Pass for Rome

There is only one pass in Rome, the Roma Pass. The Omnia is a notorious rip-off: they buy a Roma Pass, add a Vatican Museums' ticket they get on the official site, put both in a nice envelope and sell it to you at an extortionate price. You have listed only two sites that require entrance tickets: the Vatican Museums and the Archeological Colosseum Park. Buy both tickets on the 2 official sites and save money.

http://www.coopculture.it/en/the-colosseum.cfm

http://biglietteriamusei.vatican.va/musei/tickets/do

The transit authority in Rome is called ATAC, you can enter any tobacconist shop displaying ATAC's logo on the window and get a 48 hours pass. Same for automatic machines inside metro stations and most newstands.
Note that a 100 minutes BIT ticket can be used for 100 minutes on all means of transport, including transfers in any direction. During the period of validity you can enter the metro system only once, but at 1.5 € it's a bargain. You can get a bunch of BIT tickets all at once and use them when needed. Central Rome is an actraction in itself, most tourists end up walking everywhere and think they have wasted their money paying for a 48h pass.

If you want to skip the ticket lines, just get tickets in advance on the official sites. Nobody skips the security lines and there isn't a third line that travel agencies can make you skip. They would like you to believe it, but...

As Dario said, the Omnia and Turbopass Rome Card would both be a big waste of money for the very little time you'll have in Rome. As one must now make a prior reservation at the Colosseum with a Roma Pass and it doesn't cover the Vatican, that one is of no real use to you either.

Dario has provided links to the official ticketing websites for both the Colosseum/Forum/Palatine and Vatican Museums. Trevi, Spanish Steps and St. Peter's basilica are free. I'll caution that the Vatican Museums might be a miserable experience for your 4 year-old. The crowds are so dense that a young child might feel completely trampled and have difficulty seeing much. You might consider booking an early-entrance tour of that one to avoid at least some of the mob plus be able to access the basilica directly from a special inside passage reserved for tours.

As a side note, I'm a little concerned about the pace of your European trip in general. You are attempting to do a great deal with a small child in tow and little flex for things which might not go according to plan.

Thanks Dario and Kathy for the valuable responses.
Based on that now i feel i will get those BIT tickets and then individual pass for Vatican Museum + St Peter's Basicila and Colossuem +Roman Forum+Palatine Hills.
Should i get the BIT ticket/travel pass for my 4 yr old ? Also when i checked the sites mentioned by Dario for Colosseum tickets, i could find some options were we can opt for underground/panaroma/arena along with general entrance . Is it worthy to get those. Also in that it is mentioned a guide is mandatory, so how to get a authorized guide in those cases ?
When i tried booking Vatican Museum general ticket for may18th 2019, I am not seeing those dates activated. The dates are activated till May 8th only. So is it that those are already sold out or those dates are not yet open for booking. Please let me know if you have any idea about this.

Thanks in advance !

Vatican Museum tickets go on sale about 60 days in advance so it's too early for May 18th.

Booking coopculture tours of the Colosseum Underground and/or Panoramic levels has become just complex enough that I'm going to send you to this resource:

https://www.tripadvisor.com/ShowTopic-g187791-i22-k12336615-Colosseum_Underground_and_or_Upper_levels_tours_2019-Rome_Lazio.html

Donna (dbabe) is a sometimes poster on the RS forum and pretty much the authority, IMHO, regarding the ins and outs of booking those tours. Yes, it's a lot to read but she's done it more understandably than what's on the coopculture website, has provided a lot of FAQs, and she's stayed on top of the many changes to the website this past year (no small feat!). The value of seeing the underground/upper levels is really up to you.

Hi,
Thanks for sharing the link, it really had useful information.
I checked for the Colosseum Tours General Entry + Underground + Panoramic English Tours it seems i don't have tickets available for the desired dates.So i was thinking to get the Colosseum Tours General Entry + Panoramic English Tours at least. But before that , are there any chances that more seats will be added after some time.

Also if i take Colosseum Tours General Entry + Panoramic English Tours, will they restrict me from even enteringthe underground area. Or is it that there will not be a guided tour towards the underground area but i can simply roam in that underground area. Please share your feedback

Thanks in advance!!