Sleep training anyone? Sorry for the long post

I've just started this for the last week as my baby is not a fan of naps at all. I'm lucky to get 30 mins that's in my arms, never her bed. She's always been good to sleep through the night usually waking around 7am, takes a bottle and goes back to sleep for an hour or so. However I've recently tried to change this to getting up between 7am and 7. 30am in the hope that this will help with her naps during the day and so she can have an earlier bed time (most nights she would not go to bed til 10pm). So far she's been good for going into the cot for naps {3 a day) albeit after much crying but she's still only last 30 to 40 mins at the most. Last nap is not in cot it would be in car or buggy. However Bed time breaks my heart because while she is so so tired she screams until she is drained. Please tell me am I doing the right thing with this sleep training?! My whole reason was I'm due back to work soon and no one else would be able to put her down to sleep, also my husband and I could so with at least 1 night out in the near future so I'd like to make sure my mum could maybe take her overnight eventually without her screaming all night. I'm trying to remain calm but it breaks my heart to hear her upset. FTM in néed of reassurance if anyone can offer it...😭