Can I cheat on my ME1 sweetheart in ME2 and keep our romance going in ME3?

I'm playing through ME2 with FemShep carried from ME1 where I romanced Liara. As I understand there are three romance candidates for each gender in ME2 which will unlock the Paramour Achievement and have negative impact on your lover in ME3. There are also three "flirt interests" which do not unlock said achievement and will not be considered an act of adultery, if I'm correct.

In short, what I'm wondering - can I go "all in" with Kelly Chambers, Samara or Morinth and still keep my "real" love in ME3?

Yes. You can continue romances with characters from Mass Effect 1 or Mass Effect 2 regardless of who your choice was in either game. Not only that, but you can actually lead on several characters at the same time in ME3 until a so called "lock in" point. The point depends on the character, and you can find a list of them here: Mass Effect Wiki - Romance.

I am solely speaking through my own experience from my playthroughs.

I mostly play as male Sheppard.

SPOILER

In ME 1 I had a romance with with Ashley Williams, going all in on her. In ME 1, as male Sheppard, you are faced with a choice between Ashley and Liara, where I chose Ashley. Liara will still have a crush on you which you can see through her dialog.

In ME1:

My romance where Ashley Williams. (Kaiden was sacrificed no wonder)

In ME 2:

you join Cerberus. Ashley Williams is Alliance to the bone, and wont have anything to do with you, despite that she misses you when you encounter her on Horizon. So in ME 2 I had my romance with Miranda Lawson, going all in.You also encounter Liara on Illium who deep within still have a crush on you. But you are nothing more than friends here.

In ME 3:

Sheppard joins the alliance again. And Ashley Williams rejoins your crew. But, she heard about the romance from ME 2 with Miranda Lawson. She is by no doubt "pissed" about it as she still loves Sheppard. BUT, when Ashley Williams gets into the hospital, you have the option to reengage in a romance.I cant remember the exact dialog which gives you the possibility or reengaging in a romance with her.

But to conclude on your question.

YES - it is possible to continue a relationship from ME 1 in ME 3.

I can't give you detailed information regarding other romances, only that it is possible with the named characters.