A child together is not considered 100% proof your marriage is genuine - but it certainly helps. The visa office may want a DNA test to prove paternity - wait until they ask for it, as they may not and it is expensive, plus there are certain labs they insist you use.
A church wedding or not usually doesn't make any difference. I've seen cases where they questioned the marriage when the couple was very religious but didn't have a church wedding. In any case, include evidence of your wedding - both the church one and the civil one - and the reception. This includes photos, but also things like a wedding invitation, a copy of the guest list, a list of gifts received, receipts for the reception, etc.
Proof your relationship is genuine can include: photos from the beginning of your relationship until now. Ideally get some photos that are candid shots of you two, not just posed shots. Photos of either or both of you with each other's family; photos with friends; photos of trips you've taken together; and of course wedding and honeymoon photos.
Proof of contact: phone cards are not considered good contact. If you've kept them all (doubtful, I know), you can photocopy them, and include them with a letter explaining you use phone cards because they're so much cheaper. If you don't have any other phone records, and didn't keep the cards, at least explain in a letter.
If you use Skype you can get a printout of your call log; if you use some instant messenging services, you can get a printout of your call log. Emails: print out a screen shot of your and her inbox showing all the emails to each other, then print out a selection of the emails.
Any letters or cards you sent each other are good. Ideally also include the envelope so they can see when it was sent.
Proof of contact - visits: Show your tickets, boarding passes, and visa and entry and exit stamps in your passport for trips you took to see each other and trips you took together.
You're visiting her now in Ecuador - actually living with her. Show any proof of cohabitation you have. Both your names on a lease or the utility bills, a letter from the landlord stating you are living together, or similar letters from friends and relatives.
Proof of intermingled finances: If you have a joint bank account with her, show evidence of that. Evidence she is listed as a beneficiary on a will or insurance is good. Receipts for joint purchases for the home are good. Any support you have given her should be included - money transfers, Western Union receipts, money for the child, etc.
Proof of gifts: Show receipts for gifts you have given each other, and photos of the gifts.
You can also get friends and family to write letters of support. These can be affidavits, letters, or emails. They should state how they know you/your wife, when they met your spouse, what kinds of things they have done with you, and why they think your relationship is genuine.
There are several threads that talk about how to prove your relationship is genuine. I suggest you search bobshynoswife - her posts about relationship proof are very good.
