So I'm guessing that the problem here is that he's ALWAYS been cheap, but now that you're getting married you expect him to magically change ... right?
Look. Marriage won't change a person. If he was a cheap boyfriend then he'll be a cheap fiance, and a cheap husband/father. If you're not happy with that personality trait NOW, then I suggest you bail out of the relationship.
You two need to have a frank talk about money and finances before you get married, because it's clear that you don't agree on how the household money should be spent. Sit down one day (get a babysitter and clear out your whole schedule for the day - no distractions) and make a spreadsheet or use Mint.com to paint a clear picture of your finances. Mortgage/rent, bills, savings, groceries, student loans, car loans, insurance payments, utilities, medical care, pet care, clothes and haircuts, gifts, education funds for the kids, every little thing. Then look at what's left and talk about how to spend it.
Spending $2k total on a ring and a wedding is all relative. If you have money to burn, then sure, if a larger wedding means a lot to you then talk to him about it. If you're up to your eyeballs in debt, though, then a bigger engagement ring is really not your top priority right now.
Did you have a say in your engagement ring? Did he talk to you beforehand about what style you wanted? Was the size/cost discussed? If you both had a clear discussion about what you wanted, and then he went and got something totally different ... then, yes, you have a point if you say that he's not being considerate of you (it's not about the ring itself, it's about listening to you and then dismissing your feelings). But if the ring was a surprise, or if the ring is what you wanted but you never specified you wanted a bigger size ... well, it's a gift, honey, so deal with it.
The ring is just a symbol, and a gift. It's not meant to be indicative of his feelings for you or how much he values you. If you need to put a price tag on his feelings, then maybe he's not the guy for you, or maybe you're just not mature enough for marriage. If you TRULY feel that he doesn't value you, then the ring is likely just the straw that broke the camel's back ... his actions mean MUCH more than a piece of jewelry, so if he's been dismissive and uncaring of you in other aspects of the relationship then a bigger engagement ring isn't going to solve that problem.
Is your relationship OK otherwise? People have different "love languages" - one of which is gifts and spending money. Other things include quality time together (good conversations, spending time together, making time for the family), affirmations (saying "I love you" a lot, telling you often that he appreciates your hard work in the relationship/family), acts of service (he gases up your car or fixes your electronics without being asked, comes outside to help you carry in groceries, etc.), and physical touch (hugs and kisses, physical affection).
So if your guy is helpful and kind in other areas, but just isn't a big spender or a good gift-giver, then personally I'd let it go. If he's not showering you with gifts or a big diamond ring it doesn't automatically mean that he doesn't care about you.
But, again, if your relationship is failing in other areas, then a bigger ring or a fancier wedding won't solve that problem.
Him not wanting to spend a ton of money on a wedding or jewelry (especially when you have FIVE KIDS to care for - and really, at some point in your life a fancy wedding and a big engagement ring fall lower on the list of priorities, especially in second+ marriages) isn't automatically a red flag. But if he's cheaping out on you and the kids, and instead blowing his money on selfish things or gambling or foolish investments ... then you need to ask yourself if you want to spend your life with such a person.