Since there are a lot of people involved and it would be wordy to mention everyone by name (especially if you're mentioning your FILs as well), I would go with:
Together with their parents
Bride
and
Groom
request the pleasure of your company/honor of your presence
blah, blah, blah
I'd go for that option, as everyone is included without listing a bunch of names. If you want to mention everyone by name (or if they want to be mentioned by name), you have a couple other options. Since your dad and stepmom are paying for the wedding, they are technically the hosts, not your mom. Here's a couple options:
Mr. and Mrs. DadsName
request the pleasure of your company/honor of your presence
at the marriage of Mr. DadsName's daughter
Bride
to
Groom
blah, blah, blah
Mr. and Mrs. DadsName
request the pleasure of your company/honor of your presence
at the marriage of
Bride
daughter of Mr. DadsName and Mrs. MomsName
to Groom
blah, blah, blah
If your FILs want to be mentioned as well, you can add a 'son of Mr. and Mrs. TheirName' line below the groom's name on either of those.
If your mom is also contributing money towards the wedding or if your dad considers her to be cohosting, you can do the following:
Mrs. MomsName
and
Mr. and Mrs. DadsName
request the pleasure of your company/honor of your presence
at the marriage of their daughter/at the marriage of Mrs MomsName and Mr DadsName's daughter
Bride
to
Groom
son of Mr and Mrs TheirName
blah, blah, blah
If all three sets of parents are hosting, the wording would go like this:
Mrs MomsName
Mr. and Mrs. DadsName
and
Mr. and MrsILsName
request the pleasure of your company/honor of your presence
at the marriage of their children
Bride
and
Groom
blah, blah, blah

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