Autumn, I know you say your daughter comes first but that doesn't mean you can't be looked after, too
I suppose you are in the US and I don't know the guidelines there but here are the UK guidelines:
https://www.rcog.org.uk/womens-health/clinical-guidance/reducing-risk-of-thrombosis-greentop37a
If you open the document and look at page four you'll see that you fall into the middle (amber) risk category as you have known thrombophilia but no previous history of VTE (venous thromboembolism, I.e. a history of clots). This means you should be considered for low molecular weight heparin (lovenox or similar) in addition to aspirin but it might not be absolutely necessary.
If you find that you have another risk factor such as being overweight, over 35, or a smoker then maybe you ought to push for more. If you don't have further risk factors and are happy to proceed as is then educate yourself on the symptoms of a dvt or pulmonary embolism so that you can recognise them early.
Without knowing more about your individual case it sounds like neither party was entirely wrong with their opinion

One thing I would stress, though, especially if you end up having a c-section, is to have a risk assessment the. You should go on the injections for at least a week after! It's a small price to pay for your safety and the risk is quite high at that time.
I have FVL and a history of clotting as well as recurrent miscarriage. Among other things, I take baby aspirin and heparin injections every day up to six weeks after giving birth. It worked well with my son (planned c-section) and I'm hoping it will work well again. A lot of women take lovenox or similar in pregnancy so there is quite a track record.