"I love my mom a lot."
Translation:Bardzo kocham moją mamę.
Generally the object is after the verb, just not when it means that a pronoun ends up at the end of the sentence. So "Bardzo kocham moją mamę" is the more basic word order, but "Bardzo cię kocham" avoids the clunkiness of ending with a pronoun, a problem that the 'mom' sentence doesn't have.
you cannot use "duzo" in such a situation ?
No. Depending on context, in English "a lot" can replace "much" or "many", but it can also mean "greatly" "very". In this context - only the last meaning works https://www.diki.pl/a+lot . Saying
"dużo kocham moja mamę" would be similar to English "I many love my mom".