the fact you have a joint account and he flirts with women knowing you could read it, and knowing these girls will see he is with someone, is definitely a sign that he has no respect for you and couldnt care less if he is caught- he is not even trying to do it hidden!
Relationships need at least a fair amount of trust, and my bloke is definitely someone i have found hard to trust due to his drink and drug addictions- it took him to do 10 months of rehab and now out and clean for me to start trusting again, but even then i still have my bad days.
But blatantly flirting with women on the internet is not on- and this is not the first time, which means it wont be the last.
Dont stay purely due to ur furniture. Sell the furniture while he is out at work and pack up and go. You will afford lovely furniture one day and will appreciate it. If you truly dont trust him, and feel that he wont ever change, then dont put you and your child through this.
It is always a struggle when a baby comes, and for most of us that includes financially, but as long as your baby is loved by you, it doesnt matter if ur in a hostel, bnb or posh house. He will learn from you that you work hard to achieve a lovely home, which will help him with ambition when he is older.
Hope ur ok, mull all pros and cons over next few weeks and then see what ur gut tells u. Our guts are always right, we just choose to ignore them sometimes!